Time series analysis

TIME SERIES ANALYSIS

• SUBMITTED TO DR. VANDANA SARIN WALIA

GROUP MEMBERS

• Nishi aggarwal• Raman mangla • Parth kansal• Aashi• Shivam dhawan• Samarth goyal• Abhishek rawat• Neha jalan

ACKNOWLEDGEMENT • I WOULD LIKE TO THANK DR. VANDANA SARIN WALIA FOR

PROVIDING OUR TEAM A WONDERFUL OPPORTUNITY TO APPLY THE KNOWLEDGE , IN PRACTICAL TERMS .

THROUGH THIS PROJECT WE WERE ABLE TO GET THE ABSOLUTE

PRACTICAL IDEA . WITH HER HELP AND CONTINOUS GUIDENCE WE WERE ABLE TO

COMPLETE THIS PROJECT,WE HOPE THAT WE ARE ABLE TO MAKE THIS PROJECT UPTO HER

EXPECTATIONS .

THANK YOU !

Time seriesA time series is a sequence of DATA

POINTS, measured typically at successive points in time spaced at uniform time intervals.

Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data.

Examples of data could be: stock market prices, currency values, item prices, daily temperatures, weekly rainfall, population growth ETC.

COMPONENTS OF TIME SERIES

• RANDOM• CYCLICAL

• TREND• SEASONAL

ANALYSIS OF

SERIESTIME

DATA ON PRICES OF

ORANGES

MONTHS 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

JAN 97.861

1598102.46

2175108.71

2753102.89

9106112.91

5022104.21

599128.20

5549123.2129685

93.29427368

100.03885

100.5411201

111.208917

102.7792365

107.4666035

101.480888

96.41692951

98.9368017

101.7797778

FEB104.05

719395.791

333109.14

470696.789

419592.745

7724116.69

1027102.45

881392.310

7854115.7016164

115.9720052

96.67078553

105.6116624

101.882193

97.90136545

90.11530764

120.4666422

106.578335

109.2729624

102.3607515

MAR109.18

8206103.16

9179103.46

0856108.82

986492.456

5036136.26

0039129.85

1304125.36

3323112.4745804

149.3965192

98.46614564

96.37927348

117.324576

110.5145735

97.26260455

96.32525764

103.0733073

110.800654

104.8227466

APR111.46

7358107.52

3474108.68

5963101.70

5941112.80

5113.50

19298.107

838110.55

657391.89061965

105.9428705

98.94542937

105.4847536

100.2396874

106.7847235

104.1907575

103.3468631

102.5318664

107.971589

104.7988516

MAY98.354

7344104.20

0004101.10

853399.353

67121.78

7312116.61

3733109.72

960897.857

1429101.6101616

93.2517426

99.98250722

103.6221724

106.8062445

98.20015036

106.0297769

94.941939

91.85067263

107.8042611

98.59367805

JUN107.49

101193.535

968101.96

9916109.04

6708103.76

3807113.10

292299.993

7058105.02

7737105.5078774

85.30684141

83.21023757

105.4688557

107.3416357

91.88057282

113.8957628

109.5634916

126.0548007

109.5211966

99.94969939

JUL94.347

5539117.22

5696118.64

988395.010

73494.206

1948115.93

8644102.83

2549104.19

9099107.9668122

80.10035413

110.296768

122.1459576

101.2202795

87.65377641

108.4194228

106.0192056

106.5493933

96.85397141

93.82668712

AUG99.962

0817110.86

517993.345

3668106.97

199597.645

477681.477

558397.571

4264105.80

937894.106

701101.1633653

113.1318083

107.7594356

79.05691875

116.9047752

87.47859737

97.66046358

95.58985776

106.2056848

98.10099101

SEP100.22

190695.734

107998.472

770395.834

348992.962

377773.611

358998.287

327598.712

808996.33493304

98.89490362

105.75201

83.84329843

81.63360869

123.2766146

91.88294875

125.9382608

103.1430662

94.03011396

100.3723134

OCT89.644

600990.192

458886.763

1147109.77

8531104.14

850273.350

763698.021

3187106.78

9359102.2079219

108.8260817

117.9108385

94.40913759

98.46964728

111.8007663

103.7703587

86.42274926

97.99778197

89.06333726

94.95739465

NOV100.27

232484.094

271298.900

692865.709

762795.885

1095110.00

165277.619

326779.050

409677.65306122

107.8992566

89.87644788

107.3052098

93.7911478

100.1561673

75.79258414

66.00658468

86.33736045

76.81046066

98.04958

DEC91.345

080985.049

881989.650

663299.618

062784.846

654491.364

806989.505

033688.194

801795.91662706

96.57658067

85.14477189

88.54069045

89.26336513

87.80069473

87.92008259

111.1611531

89.51986208

96.60313316

107.1544987

GRAPH

Sep-95

Mar-96Sep

-96

Mar-97Sep

-97

Mar-98Sep

-98

Mar-99Sep

-99

Mar-00Sep

-00

Mar-01Sep

-01

Mar-02Sep

-02

Mar-03Sep

-03

Mar-04Sep

-04

Mar-05Sep

-05

Mar-06Sep

-06

Mar-07Sep

-07

Mar-08Sep

-08

Mar-09Sep

-09

Mar-10Sep

-10

Mar-11Sep

-11

Mar-12Sep

-12

Mar-13Sep

-13

Mar-14Sep

-14

Mar-15Sep

-150

200

400

600

800

1000

1200

1400

1600Prices of Oranges

Prices of Oranges

COMPONENTS OF TIME SERIES

SECULAR TREND• The component responsible for the general

behaviour of time series is called trend• It is a long term tendency of any particular activity to

grow or to decline.• Trend may be upward or downward.• Linear or non linear trend.

RANDOM COMPONENT•Random, irregular, erratic in nature•Cannot be foreseen•No reasons , no causes can be attributed•Causes- strikes,fire,femines etc

PERIODIC COMPONENT

SEASONAL COMPONENT

PERODIC MOVEMENT

RECCUR AFTER A TIME PERIOD OF LESS THAN ONE YEAR

CYCLICAL COMPONENT

THE PERIOD OF OSCCILATION IS MORE THAN ONE YEAR

THE CYLCES CAN BE OF DIFFERENT INTENSITY AND PERIODICITY

THERE ARE TWO TYPES OF MODELSADDITIVE MODEL• This is used when the components are independent• Yt = Tt + St + Ct + Rt

MULTIPLICATIVE MODEL• This used when components are inter-dependent.• Yt = Tt * St* Ct* Rt

• logYt = LogTt + LogSt + LogCt + LogRt

MODELS

Advantages of ANALYSING TIME SERIES .• Understanding the phenomenon under

consideration• Gaining knowledge about the Past behaviour.• Evaluate Current behaviour of the time series.• Preparing and projecting the future of time

series.

METHODS FOR MEASURING TRENDS Free hand curve method• Plot the given T.S on a graph taking a time variable t on X axis .• Join the plotted points with dotted lines• Draw a smooth line by the inspection of above graph

Method of semi averages • Divide the time series into equal halves with respect to time• Calculate the average of each halve • Semi averages are plotted against the mid points• Join the two averages.

METHOD OF MOVING AVERAGES

Moving average represents the central tendency of data in parts.The extent of moving average is determined by the period of oscillationwhenever the oscillatory movement is regular or average of period of oscillations when it is irregular.

It is appropriate to use this method when• Trend is approximately linear.• Oscillatory movement is regular.

METHOD OF FITTING MATHEMATICAL CURVES

There are many mathematical curves that can be fitted to a time series data. An examination of the plotted data often provides an adequate basis for deciding upon which type of trend to use.

The different types of curves are• A straight line• Second degree parabola• Kth degree polynomial• Exponential curves• Growth curves

Modified exponential curve Gompertz curve Logistic curve

Months yt log yt Δyt log10 yt Δ(log yt) Δ2(log yt) Δyt/Δyt-1 Δ(log yt)/Δ(log yt-1)

Sep-95 537.550 6.288 2.730

Oct-95 546.210 6.304 8.660 2.737 0.007 1.003

Nov-95 564.240 6.336 18.030 2.751 0.014 0.007 2.032 1.005

Dec-95 443.230 6.095 -121.010 2.647 -0.105 -0.119 -7.433 0.962


Jan-96 417.530 6.035 -25.700 2.621 -0.026 0.079 0.247 0.990

Feb-96 434.470 6.075 16.940 2.638 0.017 0.043 -0.666 1.007

Mar-96 474.390 6.163 39.920 2.676 0.038 0.021 2.210 1.014

Apr-96 528.790 6.271 54.400 2.723 0.047 0.009 1.235 1.018

May-96 520.090 6.255 -8.700 2.716 -0.007 -0.054 -0.153 0.997

Jun-96 559.050 6.327 38.960 2.747 0.031 0.039 -4.354 1.012

Jul-96 527.450 6.269 -31.600 2.722 -0.025 -0.057 -0.805 0.991

Aug-96 527.250 6.268 -0.200 2.722 0.000 0.025 0.007 1.000

Sep-96 528.420 6.271 1.170 2.723 0.001 0.001 -5.845 1.000

Oct-96 473.700 6.161 -54.720 2.676 -0.047 -0.048 -49.317 0.983

Nov-96 474.990 6.164 1.290 2.677 0.001 0.049 -0.025 1.000

Dec-96 433.880 6.073 -41.110 2.637 -0.039 -0.040 -33.287 0.985


Jan-97 424.600 6.052 -9.280 2.628 -0.009 0.030 0.239 0.996

Feb-97 406.730 6.009 -17.870 2.609 -0.019 -0.009 1.989 0.993

Mar-97 419.620 6.040 12.890 2.623 0.014 0.032 -0.726 1.005

Apr-97 451.190 6.113 31.570 2.654 0.032 0.018 2.325 1.012

May-97 470.140 6.154 18.950 2.672 0.018 -0.014 0.567 1.007

Jun-97 439.750 6.087 -30.390 2.643 -0.029 -0.047 -1.624 0.989

Jul-97 515.500 6.246 75.750 2.712 0.069 0.098 -2.378 1.026

Aug-97 571.510 6.349 56.010 2.757 0.045 -0.024 0.649 1.017

Sep-97 547.130 6.305 -24.380 2.738 -0.019 -0.064 -0.423 0.993

Oct-97 493.470 6.202 -53.660 2.693 -0.045 -0.026 2.368 0.984

Nov-97 414.980 6.029 -78.490 2.618 -0.075 -0.030 1.678 0.972

Dec-97 352.940 5.867 -62.040 2.548 -0.070 0.005 0.935 0.973


Jan-98 361.630 5.891 8.690 2.558 0.011 0.081 -0.150 1.004

Feb-98 394.700 5.979 33.070 2.596 0.038 0.027 3.598 1.015

Mar-98 408.360 6.013 13.660 2.611 0.015 -0.023 0.389 1.006

Apr-98 443.830 6.096 35.470 2.647 0.036 0.021 2.448 1.014

May-98 448.750 6.107 4.920 2.652 0.005 -0.031 0.132 1.002

Jun-98 457.590 6.127 8.840 2.660 0.008 0.004 1.770 1.003

Jul-98 542.930 6.298 85.340 2.735 0.074 0.066 8.766 1.028

Aug-98 506.800 6.229 -36.130 2.705 -0.030 -0.104 -0.403 0.989

Sep-98 499.060 6.213 -7.740 2.698 -0.007 0.023 0.223 0.998

Oct-98 433.000 6.071 -66.060 2.636 -0.062 -0.055 9.226 0.977

Nov-98 428.240 6.060 -4.760 2.632 -0.005 0.057 0.078 0.998

Dec-98 383.920 5.951 -44.320 2.584 -0.047 -0.043 9.883 0.982


Jan-99 417.370 6.035 33.450 2.621 0.036 0.084 -0.765 1.014

Feb-99 403.970 6.002 -13.400 2.606 -0.014 -0.050 -0.391 0.995

Mar-99 439.640 6.087 35.670 2.643 0.037 0.051 -2.593 1.014

Apr-99 447.140 6.104 7.500 2.650 0.007 -0.029 0.200 1.003

May-99 444.250 6.097 -2.890 2.648 -0.003 -0.010 -0.383 0.999

Jun-99 484.440 6.184 40.190 2.685 0.038 0.040 -13.356 1.014

Jul-99 460.270 6.132 -24.170 2.663 -0.022 -0.060 -0.591 0.992

Aug-99 492.360 6.200 32.090 2.692 0.029 0.051 -1.317 1.011

Sep-99 471.850 6.157 -20.510 2.674 -0.018 -0.048 -0.631 0.993

Oct-99 517.990 6.251 46.140 2.714 0.041 0.059 -2.193 1.015

Nov-99 340.370 5.831 -177.620 2.532 -0.182 -0.223 -4.501 0.933

Dec-99 339.070 5.827 -1.300 2.530 -0.002 0.181 0.009 0.999


Jan-00 348.900 5.855 9.830 2.543 0.012 0.014 -7.468 1.005

Feb-00 323.590 5.780 -25.310 2.510 -0.033 -0.045 -2.635 0.987

Mar-00 299.180 5.702 -24.410 2.476 -0.034 -0.001 1.041 0.986

Apr-00 337.490 5.822 38.310 2.528 0.052 0.086 -1.536 1.021

May-00 411.020 6.019 73.530 2.614 0.086 0.033 1.636 1.034

Jun-00 426.490 6.056 15.470 2.630 0.016 -0.070 0.187 1.006

Jul-00 401.780 5.997 -24.710 2.604 -0.026 -0.042 -1.615 0.990

Aug-00 392.320 5.973 -9.460 2.594 -0.010 0.016 0.399 0.996

Sep-00 364.710 5.900 -27.610 2.562 -0.032 -0.021 3.063 0.988

Oct-00 379.840 5.940 15.130 2.580 0.018 0.049 -0.557 1.007

Nov-00 364.210 5.898 -15.630 2.561 -0.018 -0.036 -1.034 0.993

Dec-00 309.020 5.734 -55.190 2.490 -0.071 -0.053 3.911 0.972


Jan-01 348.930 5.855 39.910 2.543 0.053 0.124 -0.739 1.021

Feb-01 407.170 6.010 58.240 2.610 0.067 0.014 1.271 1.026

Mar-01 554.810 6.319 147.640 2.744 0.134 0.067 2.004 1.051

Apr-01 629.720 6.446 74.910 2.799 0.055 -0.079 0.409 1.020

May-01 734.340 6.600 104.620 2.866 0.067 0.012 1.214 1.024

Jun-01 830.560 6.723 96.220 2.919 0.053 -0.013 0.801 1.019

Jul-01 962.940 6.871 132.380 2.984 0.064 0.011 1.201 1.022

Aug-01 784.580 6.666 -178.360 2.895 -0.089 -0.153 -1.385 0.970

Sep-01 577.540 6.359 -207.040 2.762 -0.133 -0.044 1.496 0.954

Oct-01 423.630 6.049 -153.910 2.627 -0.135 -0.002 1.012 0.951

Nov-01 466.000 6.145 42.370 2.668 0.041 0.176 -0.308 1.016

Dec-01 425.760 6.055 -40.240 2.629 -0.039 -0.081 -0.947 0.985


Jan-02 443.710 6.096 17.950 2.647 0.018 0.057 -0.457 1.007

Feb-02 454.620 6.120 10.910 2.658 0.011 -0.007 0.588 1.004

Mar-02 590.330 6.381 135.710 2.771 0.113 0.103 10.754 1.043

Apr-02 579.160 6.362 -11.170 2.763 -0.008 -0.122 -0.073 0.997

May-02 635.510 6.455 56.350 2.803 0.040 0.049 -4.860 1.015

Jun-02 635.470 6.455 -0.040 2.803 0.000 -0.040 -0.001 1.000

Jul-02 653.470 6.483 18.000 2.815 0.012 0.012 -443.759 1.004

Aug-02 637.600 6.458 -15.870 2.805 -0.011 -0.023 -0.880 0.996

Sep-02 626.680 6.441 -10.920 2.797 -0.008 0.003 0.703 0.997

Oct-02 614.280 6.421 -12.400 2.788 -0.009 -0.001 1.157 0.997

Nov-02 476.800 6.168 -137.480 2.678 -0.110 -0.101 12.677 0.961

Dec-02 426.760 6.057 -50.040 2.630 -0.048 0.062 0.438 0.982


Jan-03 547.130 6.305 120.370 2.738 0.108 0.156 -2.241 1.041

Feb-03 505.060 6.225 -42.070 2.703 -0.035 -0.143 -0.322 0.987

Mar-03 633.160 6.451 128.100 2.802 0.098 0.133 -2.825 1.036

Apr-03 700.000 6.552 66.840 2.845 0.044 -0.055 0.444 1.016

May-03 685.000 6.530 -15.000 2.836 -0.009 -0.053 -0.216 0.997

Jun-03 719.440 6.579 34.440 2.857 0.021 0.031 -2.265 1.008

Jul-03 749.650 6.620 30.210 2.875 0.018 -0.003 0.839 1.006

Aug-03 793.200 6.677 43.550 2.899 0.025 0.007 1.373 1.009

Sep-03 782.990 6.664 -10.210 2.894 -0.006 -0.030 -0.229 0.998

Oct-03 836.150 6.730 53.160 2.922 0.029 0.034 -5.070 1.010

Nov-03 660.980 6.494 -175.170 2.820 -0.102 -0.131 -3.579 0.965

Dec-03 582.950 6.369 -78.030 2.766 -0.055 0.048 0.534 0.981


Jan-04 718.270 6.578 135.320 2.856 0.091 0.145 -1.662 1.033

Feb-04 831.050 6.723 112.780 2.920 0.063 -0.027 0.699 1.022

Mar-04 934.720 6.841 103.670 2.971 0.051 -0.012 0.806 1.017

Apr-04 858.920 6.756 -75.800 2.934 -0.037 -0.088 -0.719 0.988

May-04 872.750 6.772 13.830 2.941 0.007 0.044 -0.189 1.002

Jun-04 920.820 6.826 48.070 2.964 0.023 0.016 3.357 1.008

Jul-04 994.180 6.903 73.360 2.997 0.033 0.010 1.430 1.011

Aug-04 935.590 6.842 -58.590 2.971 -0.026 -0.060 -0.792 0.991

Sep-04 901.300 6.805 -34.290 2.955 -0.016 0.010 0.615 0.995

Oct-04 921.200 6.826 19.900 2.964 0.009 0.026 -0.585 1.003

Nov-04 715.340 6.573 -205.860 2.855 -0.110 -0.119 -11.581 0.963

Dec-04 686.130 6.532 -29.210 2.836 -0.018 0.092 0.165 0.994


Jan-05 640.120 6.462 -46.010 2.806 -0.030 -0.012 1.665 0.989

Feb-05 742.360 6.611 102.240 2.871 0.064 0.094 -2.135 1.023

Mar-05 1109.060 7.012 366.700 3.045 0.174 0.110 2.709 1.061

Apr-05 1174.970 7.070 65.910 3.070 0.025 -0.149 0.144 1.008

May-05 1095.680 7.000 -79.290 3.040 -0.030 -0.055 -1.210 0.990

Jun-05 934.690 6.841 -160.990 2.971 -0.069 -0.039 2.275 0.977

Jul-05 748.690 6.619 -186.000 2.874 -0.096 -0.027 1.396 0.968

Aug-05 757.400 6.631 8.710 2.879 0.005 0.101 -0.052 1.002

Sep-05 749.030 6.619 -8.370 2.874 -0.005 -0.010 -0.961 0.998

Oct-05 815.140 6.704 66.110 2.911 0.037 0.042 -7.611 1.013

Nov-05 879.530 6.780 64.390 2.944 0.033 -0.004 0.899 1.011

Dec-05 849.420 6.745 -30.110 2.929 -0.015 -0.048 -0.458 0.995


Jan-06 849.750 6.746 0.330 2.929 0.000 0.015 -0.011 1.000

Feb-06 821.460 6.712 -28.290 2.915 -0.015 -0.015 -87.170 0.995

Mar-06 808.860 6.696 -12.600 2.908 -0.007 0.008 0.457 0.998

Apr-06 800.330 6.686 -8.530 2.903 -0.005 0.002 0.686 0.998

May-06 800.190 6.686 -0.140 2.903 0.000 0.005 0.017 1.000

Jun-06 665.840 6.502 -134.350 2.823 -0.080 -0.080 1050.626 0.973

Jul-06 734.400 6.600 68.560 2.866 0.043 0.122 -0.533 1.015

Aug-06 830.840 6.723 96.440 2.920 0.054 0.011 1.259 1.019

Sep-06 878.630 6.779 47.790 2.944 0.024 -0.029 0.453 1.008

Oct-06 1036.000 6.944 157.370 3.015 0.072 0.047 2.946 1.024

Nov-06 931.120 6.837 -104.880 2.969 -0.046 -0.118 -0.648 0.985

Dec-06 792.800 6.676 -138.320 2.899 -0.070 -0.023 1.507 0.976


Jan-07 797.090 6.682 4.290 2.902 0.002 0.072 -0.034 1.001

Feb-07 841.820 6.736 44.730 2.925 0.024 0.021 10.117 1.008

Mar-07 811.340 6.699 -30.480 2.909 -0.016 -0.040 -0.675 0.995

Apr-07 855.840 6.753 44.500 2.932 0.023 0.039 -1.448 1.008

May-07 886.840 6.788 31.000 2.948 0.015 -0.008 0.666 1.005

Jun-07 935.340 6.842 48.500 2.971 0.023 0.008 1.496 1.008

Jul-07 1142.480 7.042 207.140 3.058 0.087 0.064 3.757 1.029

Aug-07 1231.130 7.116 88.650 3.090 0.032 -0.054 0.374 1.011

Sep-07 1032.220 6.940 -198.910 3.014 -0.077 -0.109 -2.358 0.975

Oct-07 974.510 6.883 -57.710 2.989 -0.025 0.052 0.326 0.992

Nov-07 1045.700 6.953 71.190 3.019 0.031 0.056 -1.226 1.010

Dec-07 925.870 6.831 -119.830 2.967 -0.053 -0.083 -1.726 0.982


Jan-08 1029.650 6.938 103.780 3.013 0.046 0.099 -0.873 1.016

Feb-08 1049.030 6.956 19.380 3.021 0.008 -0.038 0.176 1.003

Mar-08 1230.770 7.116 181.740 3.090 0.069 0.061 8.568 1.023

Apr-08 1233.720 7.119 2.950 3.091 0.001 -0.068 0.015 1.000

May-08 1317.690 7.184 83.970 3.120 0.029 0.028 27.505 1.009

Jun-08 1414.430 7.255 96.740 3.151 0.031 0.002 1.076 1.010

Jul-08 1431.690 7.267 17.260 3.156 0.005 -0.026 0.171 1.002

Aug-08 1131.850 7.032 -299.840 3.054 -0.102 -0.107 -19.375 0.968

Sep-08 923.970 6.829 -207.880 2.966 -0.088 0.014 0.864 0.971

Oct-08 909.830 6.814 -14.140 2.959 -0.007 0.081 0.076 0.998

Nov-08 853.340 6.750 -56.490 2.931 -0.028 -0.021 4.156 0.991

Dec-08 761.720 6.636 -91.620 2.882 -0.049 -0.021 1.772 0.983


Jan-09 782.890 6.664 21.170 2.894 0.012 0.061 -0.241 1.004

Feb-09 766.460 6.642 -16.430 2.884 -0.009 -0.021 -0.774 0.997

Mar-09 847.050 6.742 80.590 2.928 0.043 0.053 -4.714 1.015

Apr-09 904.520 6.808 57.470 2.956 0.029 -0.015 0.657 1.010

May-09 888.240 6.790 -16.280 2.949 -0.008 -0.036 -0.277 0.997

Jun-09 816.120 6.705 -72.120 2.912 -0.037 -0.029 4.662 0.988

Jul-09 715.360 6.573 -100.760 2.855 -0.057 -0.020 1.556 0.980

Aug-09 836.290 6.730 120.930 2.922 0.068 0.125 -1.185 1.024

Sep-09 1030.950 6.939 194.660 3.013 0.091 0.023 1.340 1.031

Oct-09 1152.610 7.051 121.660 3.062 0.048 -0.042 0.533 1.016

Nov-09 1154.410 7.052 1.800 3.062 0.001 -0.048 0.014 1.000

Dec-09 1013.580 6.922 -140.830 3.006 -0.057 -0.057 -83.374 0.982


Jan-10 1089.260 6.994 75.680 3.037 0.031 0.088 -0.553 1.010

Feb-10 981.590 6.890 -107.670 2.992 -0.045 -0.076 -1.445 0.985

Mar-10 954.720 6.862 -26.870 2.980 -0.012 0.033 0.267 0.996

Apr-10 994.730 6.903 40.010 2.998 0.018 0.030 -1.479 1.006

May-10 1054.710 6.962 59.980 3.023 0.025 0.008 1.426 1.008

Jun-10 1201.270 7.092 146.560 3.080 0.057 0.031 2.222 1.019

Jul-10 1302.410 7.173 101.140 3.115 0.035 -0.021 0.621 1.011

Aug-10 1139.330 7.039 -163.080 3.057 -0.058 -0.093 -1.655 0.981

Sep-10 1046.850 6.954 -92.480 3.020 -0.037 0.021 0.633 0.988

Oct-10 1086.320 6.991 39.470 3.036 0.016 0.053 -0.437 1.005

Nov-10 823.350 6.714 -262.970 2.916 -0.120 -0.136 -7.489 0.960

Dec-10 723.890 6.585 -99.460 2.860 -0.056 0.064 0.464 0.981


Jan-11 734.610 6.600 10.720 2.866 0.006 0.062 -0.114 1.002

Feb-11 884.960 6.786 150.350 2.947 0.081 0.074 12.667 1.028

Mar-11 852.440 6.749 -32.520 2.931 -0.016 -0.097 -0.201 0.994

Apr-11 880.970 6.782 28.530 2.945 0.014 0.031 -0.879 1.005

May-11 836.410 6.730 -44.560 2.922 -0.023 -0.037 -1.577 0.992

Jun-11 916.400 6.821 79.990 2.962 0.040 0.062 -1.760 1.014

Jul-11 971.560 6.880 55.160 2.987 0.025 -0.014 0.640 1.009

Aug-11 948.830 6.856 -22.730 2.977 -0.010 -0.036 -0.405 0.997

Sep-11 1194.940 7.087 246.110 3.077 0.100 0.110 -9.742 1.034

Oct-11 1032.700 6.941 -162.240 3.014 -0.063 -0.164 -0.633 0.979

Nov-11 681.650 6.525 -351.050 2.834 -0.180 -0.117 2.847 0.940

Dec-11 757.730 6.631 76.080 2.880 0.046 0.226 -0.255 1.016


Jan-12 730.580 6.595 -27.150 2.864 -0.016 -0.062 -0.345 0.994

Feb-12 778.640 6.658 48.060 2.891 0.028 0.044 -1.746 1.010

Mar-12 802.570 6.689 23.930 2.904 0.013 -0.015 0.475 1.005

Apr-12 822.890 6.714 20.320 2.915 0.011 -0.002 0.826 1.004

May-12 755.830 6.629 -67.060 2.878 -0.037 -0.048 -3.400 0.987

Jun-12 952.760 6.860 196.930 2.979 0.101 0.137 -2.724 1.035

Jul-12 1015.160 6.924 62.400 3.007 0.028 -0.073 0.274 1.009

Aug-12 970.390 6.878 -44.770 2.987 -0.020 -0.047 -0.711 0.993

Sep-12 1000.890 6.909 30.500 3.000 0.013 0.033 -0.686 1.004

Oct-12 980.850 6.889 -20.040 2.992 -0.009 -0.022 -0.654 0.997

Nov-12 846.840 6.742 -134.010 2.928 -0.064 -0.055 7.264 0.979

Dec-12 758.090 6.631 -88.750 2.880 -0.048 0.016 0.754 0.984


Jan-13 750.030 6.621 -8.060 2.875 -0.005 0.043 0.097 0.998

Feb-13 819.580 6.709 69.550 2.914 0.039 0.043 -8.296 1.013

Mar-13 908.100 6.812 88.520 2.958 0.045 0.006 1.157 1.015

Apr-13 980.490 6.889 72.390 2.991 0.033 -0.011 0.748 1.011

May-13 1057.010 6.964 76.520 3.024 0.033 -0.001 0.980 1.011

Jun-13 1157.650 7.055 100.640 3.064 0.039 0.007 1.210 1.013

Jul-13 1121.230 7.023 -36.420 3.050 -0.014 -0.053 -0.351 0.995

Aug-13 1190.810 7.083 69.580 3.076 0.026 0.040 -1.883 1.009

Sep-13 1119.720 7.022 -71.090 3.049 -0.027 -0.053 -1.022 0.991

Oct-13 997.260 6.906 -122.460 2.999 -0.050 -0.024 1.882 0.984

Nov-13 766.000 6.642 -231.260 2.884 -0.115 -0.064 2.278 0.962

Dec-13 739.980 6.607 -26.020 2.869 -0.015 0.100 0.131 0.995


Jan-14 753.150 6.625 13.170 2.877 0.008 0.023 -0.510 1.003

Feb-14 770.930 6.648 17.780 2.887 0.010 0.002 1.323 1.004

Mar-14 808.110 6.695 37.180 2.907 0.020 0.010 2.019 1.007

Apr-14 846.890 6.742 38.780 2.928 0.020 0.000 0.995 1.007

May-14 834.980 6.728 -11.910 2.922 -0.006 -0.027 -0.302 0.998

Jun-14 834.560 6.728 -0.420 2.921 0.000 0.006 0.036 1.000

Jul-14 783.040 6.664 -51.520 2.894 -0.028 -0.027 126.648 0.991

Aug-14 768.170 6.645 -14.870 2.885 -0.008 0.019 0.301 0.997

Sep-14 771.030 6.648 2.860 2.887 0.002 0.010 -0.194 1.001

Oct-14 732.150 6.597 -38.880 2.865 -0.022 -0.024 -13.923 0.992

Nov-14 717.870 6.577 -14.280 2.856 -0.009 0.014 0.381 0.997

Dec-14 769.230 6.646 51.360 2.886 0.030 0.039 -3.508 1.011


Jan-15 758.020 6.631 -11.210 2.880 -0.006 -0.036 -0.212 0.998

Feb-15 704.170 6.558 -53.850 2.848 -0.032 -0.026 5.020 0.989

Mar-15 633.290 6.452 -70.880 2.802 -0.046 -0.014 1.440 0.984

Apr-15 612.130 6.418 -21.160 2.787 -0.015 0.031 0.320 0.995

May-15 608.640 6.412 -3.490 2.784 -0.002 0.012 0.168 0.999

Jun-15 629.900 6.446 21.260 2.799 0.015 0.017 -6.005 1.005

Jul-15 640.110 6.462 10.210 2.806 0.007 -0.008 0.468 1.002

Aug-15 684.280 6.529 44.170 2.835 0.029 0.022 4.150 1.010

Sep-15 631.910 6.449 -52.370 2.801 -0.035 -0.064 -1.193 0.988

GOMPERTZ CURVEGompertz curve can be fitted by two method. These are :

Method of 3 selected points

Method of partial sums :

In this method the time series data is divided into 3 equal parts. For this purpose one or two values may be ignored from the data depending upon the relevance of future or past data.

Now the sums of values of 3 equal parts namely S1 ,S2 and S3 are used to estimate values of k , A and b as shown below.

S1 490.6460564

S2 538.1634728

S3 541.2514735

K 6.768326256

A -1.889290886

b 0.966407534

k 869.8547604

a 0.151178974

Months K+Abt Trend Values

Jan-96 5.176 176.929

Feb-96 5.229 186.652

Mar-96 5.281 196.556

Apr-96 5.331 206.627

May-96 5.379 216.849

Jun-96 5.426 227.208

Jul-96 5.471 237.689

Aug-96 5.515 248.276

Sep-96 5.557 258.957

Oct-96 5.597 269.714

Nov-96 5.637 280.535

Dec-96 5.675 291.405


Sep-95 4.943 140.120

Oct-95 5.004 148.983

Nov-95 5.063 158.081

Dec-95 5.120 167.401


Jan-97 5.711 302.309

Feb-97 5.747 313.235

Mar-97 5.781 324.169

Apr-97 5.814 335.098

May-97 5.846 346.009

Jun-97 5.877 356.892

Jul-97 5.907 367.734

Aug-97 5.936 378.525

Sep-97 5.964 389.254

Oct-97 5.991 399.912

Nov-97 6.017 410.489

Dec-97 6.043 420.976


Jan-98 6.067 431.365

Feb-98 6.091 441.649

Mar-98 6.113 451.821

Apr-98 6.135 461.873

May-98 6.157 471.800

Jun-98 6.177 481.596

Jul-98 6.197 491.257

Aug-98 6.216 500.777

Sep-98 6.235 510.152

Oct-98 6.253 519.379

Nov-98 6.270 528.455

Dec-98 6.287 537.376


Jan-99 6.303 546.141

Feb-99 6.319 554.748

Mar-99 6.334 563.194

Apr-99 6.348 571.478

May-99 6.362 579.600

Jun-99 6.376 587.559

Jul-99 6.389 595.354

Aug-99 6.402 602.986

Sep-99 6.414 610.454

Oct-99 6.426 617.760

Nov-99 6.438 624.902

Dec-99 6.449 631.884


Jan-00 6.459 638.705

Feb-00 6.470 645.367

Mar-00 6.480 651.871

Apr-00 6.490 658.219

May-00 6.499 664.412

Jun-00 6.508 670.452

Jul-00 6.517 676.342

Aug-00 6.525 682.084

Sep-00 6.533 687.678

Oct-00 6.541 693.129

Nov-00 6.549 698.437

Dec-00 6.556 703.605


Jan-01 6.563 708.637

Feb-01 6.570 713.533

Mar-01 6.577 718.297

Apr-01 6.583 722.931

May-01 6.590 727.438

Jun-01 6.596 731.821

Jul-01 6.601 736.081

Aug-01 6.607 740.222

Sep-01 6.612 744.245

Oct-01 6.618 748.154

Nov-01 6.623 751.952

Dec-01 6.628 755.640


Jan-02 6.632 759.222

Feb-02 6.637 762.699

Mar-02 6.641 766.075

Apr-02 6.646 769.351

May-02 6.650 772.531

Jun-02 6.654 775.616

Jul-02 6.658 778.610

Aug-02 6.661 781.513

Sep-02 6.665 784.330

Oct-02 6.668 787.062

Nov-02 6.672 789.711

Dec-02 6.675 792.279


Jan-03 6.678 794.769

Feb-03 6.681 797.183

Mar-03 6.684 799.523

Apr-03 6.687 801.790

May-03 6.690 803.988

Jun-03 6.692 806.117

Jul-03 6.695 808.181

Aug-03 6.697 810.180

Sep-03 6.700 812.116

Oct-03 6.702 813.992

Nov-03 6.704 815.809

Dec-03 6.706 817.569


Jan-04 6.708 819.273

Feb-04 6.710 820.924

Mar-04 6.712 822.522

Apr-04 6.714 824.069

May-04 6.716 825.567

Jun-04 6.718 827.018

Jul-04 6.720 828.422

Aug-04 6.721 829.781

Sep-04 6.723 831.097

Oct-04 6.724 832.370

Nov-04 6.726 833.603

Dec-04 6.727 834.796


Jan-05 6.729 835.950

Feb-05 6.730 837.068

Mar-05 6.731 838.149

Apr-05 6.732 839.195

May-05 6.734 840.207

Jun-05 6.735 841.186

Jul-05 6.736 842.134

Aug-05 6.737 843.051

Sep-05 6.738 843.937

Oct-05 6.739 844.795

Nov-05 6.740 845.625

Dec-05 6.741 846.428


Jan-06 6.742 847.205

Feb-06 6.743 847.956

Mar-06 6.744 848.683

Apr-06 6.745 849.385

May-06 6.745 850.065

Jun-06 6.746 850.723

Jul-06 6.747 851.358

Aug-06 6.748 851.973

Sep-06 6.748 852.568

Oct-06 6.749 853.143

Nov-06 6.750 853.699

Dec-06 6.750 854.237


Jan-07 6.751 854.757

Feb-07 6.751 855.260

Mar-07 6.752 855.746

Apr-07 6.753 856.216

May-07 6.753 856.671

Jun-07 6.754 857.111

Jul-07 6.754 857.536

Aug-07 6.755 857.947

Sep-07 6.755 858.344

Oct-07 6.755 858.728

Nov-07 6.756 859.100

Dec-07 6.756 859.459


Jan-08 6.757 859.806

Feb-08 6.757 860.142

Mar-08 6.757 860.466

Apr-08 6.758 860.780

May-08 6.758 861.083

Jun-08 6.759 861.376

Jul-08 6.759 861.660

Aug-08 6.759 861.934

Sep-08 6.759 862.199

Oct-08 6.760 862.455

Nov-08 6.760 862.703

Dec-08 6.760 862.942


Jan-09 6.761 863.173

Feb-09 6.761 863.397

Mar-09 6.761 863.613

Apr-09 6.761 863.822

May-09 6.762 864.024

Jun-09 6.762 864.219

Jul-09 6.762 864.408

Aug-09 6.762 864.590

Sep-09 6.762 864.767

Oct-09 6.763 864.937

Nov-09 6.763 865.102

Dec-09 6.763 865.261


Jan-10 6.763 865.415

Feb-10 6.763 865.564

Mar-10 6.764 865.707

Apr-10 6.764 865.846

May-10 6.764 865.981

Jun-10 6.764 866.111

Jul-10 6.764 866.236

Aug-10 6.764 866.358

Sep-10 6.764 866.475

Oct-10 6.765 866.588

Nov-10 6.765 866.698

Dec-10 6.765 866.804


Jan-11 6.765 866.906

Feb-11 6.765 867.005

Mar-11 6.765 867.100

Apr-11 6.765 867.193

May-11 6.765 867.282

Jun-11 6.765 867.368

Jul-11 6.766 867.452

Aug-11 6.766 867.532

Sep-11 6.766 867.610

Oct-11 6.766 867.686

Nov-11 6.766 867.758

Dec-11 6.766 867.829


Jan-12 6.766 867.897

Feb-12 6.766 867.962

Mar-12 6.766 868.026

Apr-12 6.766 868.087

May-12 6.766 868.147

Jun-12 6.766 868.204

Jul-12 6.766 868.259

Aug-12 6.767 868.313

Sep-12 6.767 868.365

Oct-12 6.767 868.415

Nov-12 6.767 868.463

Dec-12 6.767 868.510


Jan-13 6.767 868.555

Feb-13 6.767 868.598

Mar-13 6.767 868.641

Apr-13 6.767 868.681

May-13 6.767 868.721

Jun-13 6.767 868.759

Jul-13 6.767 868.796

Aug-13 6.767 868.831

Sep-13 6.767 868.866

Oct-13 6.767 868.899

Nov-13 6.767 868.931

Dec-13 6.767 868.962


Jan-14 6.767 868.992

Feb-14 6.767 869.021

Mar-14 6.767 869.049

Apr-14 6.767 869.076

May-14 6.767 869.102

Jun-14 6.767 869.127

Jul-14 6.768 869.152

Aug-14 6.768 869.175

Sep-14 6.768 869.198

Oct-14 6.768 869.220

Nov-14 6.768 869.242

Dec-14 6.768 869.262


Jan-15 6.768 869.282

Feb-15 6.768 869.301

Mar-15 6.768 869.320

Apr-15 6.768 869.338

May-15 6.768 869.355

Jun-15 6.768 869.372

Jul-15 6.768 869.388

Aug-15 6.768 869.404

Sep-15 6.768 869.419

Sep-95

Apr-96

Nov-96Jun-97

Jan-98

Aug-98

Mar-99Oct-

99

May-00

Dec-00

Jul-01Feb

-02Sep

-02

Apr-03

Nov-03Jun-04

Jan-05

Aug-05

Mar-06Oct-

06

May-07

Dec-07

Jul-08Feb

-09Sep

-09

Apr-10

Nov-10Jun-11

Jan-12

Aug-12

Mar-13Oct-

13

May-14

Dec-14

Jul-15

0

200

400

600

800

1000

1200

1400

1600

Prices of OrangesTrendline

MEASUREMENT OF SEASONAL COMPONENT

ESTIMATION OF SEASONAL COMPONENT

• Seasonal variation is measured in terms of an index, called a seasonal index. Its an average that can be used to compare actual observation relative to what it would be if there were no seasonal variations .

• An index value is attached to each period of time series within a year.

• The following methods are used Method of simple averages Ratio to trend method Ratio to moving average method Link relative method

METHOD OF SIMPLE AVERAGES

• This is the simplest method of measuring seasonal component

• This method assumes that the data does not contain trend or cyclic component.

Ratio to trend method

• This method is an improvement over the simple averages method and is based on the assumption that seasonal variation for any given month is constant factor of the trend.

Ratio to moving averages method

• Moving averages completely eliminates the seasonal movements if the extent of the moving averages is equal to the oscillatory movements sought to be eliminated.

• Some of the seasonal indices cannot be determined.

Link relative method

• This method is based on averaging the link relatives.

• Link relative is the value of one season expressed as a percentage of the value of the preceding season.

Link relative method

Months/Years 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Jan 94.20166 97.86116 102.4622 108.7128 102.8991 112.915 104.216 128.2055 123.213 93.29427

Feb 104.0572 95.79133 109.1447 96.78942 92.74577 116.691 102.4588 92.31079 115.7016 115.972

Mar 109.1882 103.1692 103.4609 108.8299 92.4565 136.26 129.8513 125.3633 112.4746 149.3965

Apr 111.4674 107.5235 108.686 101.7059 112.805 113.5019 98.10784 110.5566 91.89062 105.9429

May 98.35473 104.2 101.1085 99.35367 121.7873 116.6137 109.7296 97.85714 101.6102 93.25174

Jun 107.491 93.53597 101.9699 109.0467 103.7638 113.1029 99.99371 105.0277 105.5079 85.30684

Jul 94.34755 117.2257 118.6499 95.01073 94.20619 115.9386 102.8325 104.1991 107.9668 80.10035

Aug 99.96208 110.8652 93.34537 106.972 97.64548 81.47756 97.57143 105.8094 94.1067 101.1634

Sep 100.2219 95.73411 98.47277 95.83435 92.96238 73.61136 98.28733 98.71281 96.33493 98.8949

Oct 101.611 89.6446 90.19246 86.76311 109.7785 104.1485 73.35076 98.02132 106.7894 102.2079 108.8261

Nov 103.3009 100.2723 84.09427 98.90069 65.70976 95.88511 110.0017 77.61933 79.05041 77.65306 107.8993

Dec 78.55345 91.34508 85.04988 89.65066 99.61806 84.84665 91.36481 89.50503 88.1948 95.91663 96.57658

Months/Years 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Jan 100.0389 100.5411 111.2089 102.7792 107.4666 101.4809 96.41693 98.9368 101.7798 98.5427

Feb 96.67079 105.6117 101.8822 97.90137 90.11531 120.4666 106.5783 109.273 102.3608 92.89597

Mar 98.46615 96.37927 117.3246 110.5146 97.2626 96.32526 103.0733 110.8007 104.8227 89.93425

Apr 98.94543 105.4848 100.2397 106.7847 104.1908 103.3469 102.5319 107.9716 104.7989 96.65872

May 99.98251 103.6222 106.8062 98.20015 106.0298 94.94194 91.85067 107.8043 98.59368 99.42986

Jun 83.21024 105.4689 107.3416 91.88057 113.8958 109.5635 126.0548 109.5212 99.9497 103.493

Jul 110.2968 122.146 101.2203 87.65378 108.4194 106.0192 106.5494 96.85397 93.82669 101.6209

Aug 113.1318 107.7594 79.05692 116.9048 87.4786 97.66046 95.58986 106.2057 98.10099 106.9004

Sep 105.752 83.8433 81.63361 123.2766 91.88295 125.9383 103.1431 94.03011 100.3723 92.3467

Oct 117.9108 94.40914 98.46965 111.8008 103.7704 86.42275 97.99778 89.06334 94.95739

Nov 89.87645 107.3052 93.79115 100.1562 75.79258 66.00658 86.33736 76.81046 98.04958

Dec 85.14477 88.54069 89.26337 87.80069 87.92008 111.1612 89.51986 96.60313 107.1545

Months Avg Link Relative Chain Relative D ValuesCorrected CR Seasonal Indices

Jan 104.3586238 100 100 87.50457237

Feb 103.2709321 103.2709321 0.60077309 102.0693859 89.31537968

Mar 109.7676881 113.3581147 1.20154618 111.5557954 97.6164217

Apr 104.6570399 118.6372473 1.80231927 116.2341549 101.7102002

May 102.5563952 121.6700842 2.40309236 118.6662187 103.8383672

Jun 103.7562891 126.2403643 3.00386545 122.6357257 107.3118674

Jul 103.2541937 130.3484703 3.60463854 126.1430587 110.380944

Aug 99.8853719 130.1990543 4.20541163 125.3928696 109.7244943

Sep 97.56428889 127.0277815 4.80618472 121.6208237 106.4237817

Oct 98.30678381 124.8769265 5.40695781 118.8691956 104.0159813

Nov 89.7256169 112.0465927 6.0077309 105.4380887 92.26314862

Dec 91.68649486 102.7315934 6.60850399 102.7315934 89.89484152

Average 114.2797425

NEW CHAIN RELATIVE FOR FIRST MONTH 107.2092771

ResidualsResidual after trend is eliminated

t Months Yt Trend Values Seasonal Indices Residual= (Yt/Tt)*100 Residual

1 Sep-95 537.55 140.1202958 106.4237817 383.6346455 3.83634646

2 Oct-95 546.21 148.9834567 104.0159813 366.6245985 3.66624599

3 Nov-95 564.24 158.0812077 92.26314862 356.9304714 3.56930471

4 Dec-95 443.23 167.4008658 89.89484152 264.7716293 2.64771629


5 Jan-96 417.53 176.9291779 87.50457237 235.9870796 2.3598708

6 Feb-96 434.47 186.6524081 89.31537968 232.7695659 2.32769566

7 Mar-96 474.39 196.5564243 97.6164217 241.3505443 2.41350544

8 Apr-96 528.79 206.6267836 101.7102002 255.9155163 2.55915516

9 May-96 520.09 216.8488146 103.8383672 239.8399092 2.39839909

10 Jun-96 559.05 227.2076975 107.3118674 246.0524032 2.46052403

11 Jul-96 527.45 237.6885408 110.380944 221.9080475 2.21908048

12 Aug-96 527.25 248.2764534 109.7244943 212.3640776 2.12364078

13 Sep-96 528.42 258.9566136 106.4237817 204.0573487 2.04057349

14 Oct-96 473.7 269.7143327 104.0159813 175.630266 1.75630266

15 Nov-96 474.99 280.5351144 92.26314862 169.3157026 1.69315703

16 Dec-96 433.88 291.4047095 89.89484152 148.8925834 1.48892583


17 Jan-97 424.6 302.3091651 87.50457237 140.452242 1.40452242

18 Feb-97 406.73 313.2348696 89.31537968 129.8482511 1.29848251

19 Mar-97 419.62 324.1685924 97.6164217 129.4449894 1.29444989

20 Apr-97 451.19 335.0975192 101.7102002 134.6443868 1.34644387

21 May-97 470.14 346.009282 103.8383672 135.8749677 1.35874968

22 Jun-97 439.75 356.8919852 107.3118674 123.2165524 1.23216552

23 Jul-97 515.5 367.7342273 110.380944 140.1827629 1.40182763

24 Aug-97 571.51 378.525118 109.7244943 150.9833754 1.50983375

25 Sep-97 547.13 389.2542916 106.4237817 140.5585017 1.40558502

26 Oct-97 493.47 399.9119175 104.0159813 123.3946723 1.23394672

27 Nov-97 414.98 410.4887057 92.26314862 101.0941335 1.01094134

28 Dec-97 352.94 420.9759105 89.89484152 83.83852643 0.83838526


29 Jan-98 361.63 431.3653306 87.50457237 83.83381193 0.83833812

30 Feb-98 394.7 441.6493067 89.31537968 89.36955045 0.8936955

31 Mar-98 408.36 451.8207166 97.6164217 90.38098188 0.90380982

32 Apr-98 443.83 461.8729679 101.7102002 96.09352156 0.96093522

33 May-98 448.75 471.7999893 103.8383672 95.11445743 0.95114457

34 Jun-98 457.59 481.5962196 107.3118674 95.01528071 0.95015281

35 Jul-98 542.93 491.2565955 110.380944 110.518618 1.10518618

36 Aug-98 506.8 500.7765377 109.7244943 101.2028244 1.01202824

37 Sep-98 499.06 510.1519365 106.4237817 97.82575823 0.97825758

38 Oct-98 433 519.379136 104.0159813 83.36877052 0.83368771

39 Nov-98 428.24 528.4549176 92.26314862 81.03624089 0.81036241

40 Dec-98 383.92 537.3764829 89.89484152 71.44339438 0.71443394


41 Jan-99 417.37 546.1414366 87.50457237 76.42159558 0.76421596

42 Feb-99 403.97 554.7477682 89.31537968 72.82048223 0.72820482

43 Mar-99 439.64 563.1938342 97.6164217 78.06193415 0.78061934

44 Apr-99 447.14 571.4783401 101.7102002 78.24268544 0.78242685

45 May-99 444.25 579.6003222 103.8383672 76.64764546 0.76647646

46 Jun-99 484.44 587.5591296 107.3118674 82.44957411 0.82449574

47 Jul-99 460.27 595.3544067 110.380944 77.31025332 0.77310253

48 Aug-99 492.36 602.9860755 109.7244943 81.65362685 0.81653627

49 Sep-99 471.85 610.4543182 106.4237817 77.29489103 0.77294891

50 Oct-99 517.99 617.7595608 104.0159813 83.84977471 0.83849775

51 Nov-99 340.37 624.9024566 92.26314862 54.46770074 0.54467701

52 Dec-99 339.07 631.8838701 89.89484152 53.66017651 0.53660177


53 Jan-00 348.9 638.7048617 87.50457237 54.62616945 0.54626169

54 Feb-00 323.59 645.3666728 89.31537968 50.14048813 0.50140488

55 Mar-00 299.18 651.8707115 97.6164217 45.89560394 0.45895604

56 Apr-00 337.49 658.2185387 101.7102002 51.27324439 0.51273244

57 May-00 411.02 664.4118547 103.8383672 61.86223155 0.61862232

58 Jun-00 426.49 670.4524869 107.3118674 63.61226311 0.63612263

59 Jul-00 401.78 676.3423773 110.380944 59.40482417 0.59404824

60 Aug-00 392.32 682.0835712 109.7244943 57.51787853 0.57517879

61 Sep-00 364.71 687.6782064 106.4237817 53.03498011 0.5303498

62 Oct-00 379.84 693.1285024 104.0159813 54.80080515 0.54800805

63 Nov-00 364.21 698.4367507 92.26314862 52.14645416 0.52146454

64 Dec-00 309.02 703.6053056 89.89484152 43.91950964 0.4391951


65 Jan-01 348.93 708.6365756 87.50457237 49.23962607 0.49239626

66 Feb-01 407.17 713.5330147 89.31537968 57.0639328 0.57063933

67 Mar-01 554.81 718.2971148 97.6164217 77.2396253 0.77239625

68 Apr-01 629.72 722.9313988 101.7102002 87.10646696 0.87106467

69 May-01 734.34 727.4384133 103.8383672 100.948752 1.00948752

70 Jun-01 830.56 731.8207226 107.3118674 113.4922768 1.13492277

71 Jul-01 962.94 736.0809025 110.380944 130.8198592 1.30819859

72 Aug-01 784.58 740.2215354 109.7244943 105.9925931 1.05992593

73 Sep-01 577.54 744.2452043 106.4237817 77.60076876 0.77600769

74 Oct-01 423.63 748.154489 104.0159813 56.62333198 0.56623332

75 Nov-01 466 751.9519611 92.26314862 61.97204398 0.61972044

76 Dec-01 425.76 755.6401805 89.89484152 56.34427747 0.56344278


77 Jan-02 443.71 759.2216915 87.50457237 58.44274538 0.58442745

78 Feb-02 454.62 762.6990193 89.31537968 59.60673719 0.59606737

79 Mar-02 590.33 766.0746674 97.6164217 77.05906815 0.77059068

80 Apr-02 579.16 769.3511144 101.7102002 75.27902269 0.75279023

81 May-02 635.51 772.5308118 103.8383672 82.26338552 0.82263386

82 Jun-02 635.47 775.6161815 107.3118674 81.93098792 0.81930988

83 Jul-02 653.47 778.6096141 110.380944 83.92781032 0.8392781

84 Aug-02 637.6 781.5134667 109.7244943 81.58528639 0.81585286

85 Sep-02 626.68 784.3300617 106.4237817 79.90003579 0.79900036

86 Oct-02 614.28 787.0616853 104.0159813 78.04724985 0.7804725

87 Nov-02 476.8 789.7105861 92.26314862 60.37654913 0.60376549

88 Dec-02 426.76 792.2789743 89.89484152 53.86486501 0.53864865


89 Jan-03 547.13 794.7690208 87.50457237 68.84138482 0.68841385

90 Feb-03 505.06 797.1828562 89.31537968 63.3556023 0.63355602

91 Mar-03 633.16 799.5225706 97.6164217 79.19226089 0.79192261

92 Apr-03 700 801.7902129 101.7102002 87.30463265 0.87304633

93 May-03 685 803.9877904 103.8383672 85.20029883 0.85200299

94 Jun-03 719.44 806.1172688 107.3118674 89.24756085 0.89247561

95 Jul-03 749.65 808.1805719 110.380944 92.75773585 0.92757736

96 Aug-03 793.2 810.1795813 109.7244943 97.90422004 0.9790422

97 Sep-03 782.99 812.1161371 106.4237817 96.41355025 0.9641355

98 Oct-03 836.15 813.9920374 104.0159813 102.7221351 1.02722135

99 Nov-03 660.98 815.8090387 92.26314862 81.02141171 0.81021412

100 Dec-03 582.95 817.5688562 89.89484152 71.30286282 0.71302863


101 Jan-04 718.27 819.273164 87.50457237 87.67161327 0.87671613

102 Feb-04 831.05 820.9235957 89.31537968 101.233538 1.01233538

103 Mar-04 934.72 822.5217443 97.6164217 113.6407647 1.13640765

104 Apr-04 858.92 824.0691634 101.7102002 104.2291155 1.04229116

105 May-04 872.75 825.5673668 103.8383672 105.7151766 1.05715177

106 Jun-04 920.82 827.01783 107.3118674 111.3422186 1.11342219

107 Jul-04 994.18 828.4219899 110.380944 120.0088858 1.20008886

108 Aug-04 935.59 829.7812459 109.7244943 112.7514034 1.12751403

109 Sep-04 901.3 831.0969601 106.4237817 108.4470336 1.08447034

110 Oct-04 921.2 832.3704586 104.0159813 110.6718758 1.10671876

111 Nov-04 715.34 833.6030312 92.26314862 85.8130277 0.85813028

112 Dec-04 686.13 834.7959328 89.89484152 82.19134438 0.82191344


113 Jan-05 640.12 835.950384 87.50457237 76.5739226 0.76573923

114 Feb-05 742.36 837.0675712 89.31537968 88.68579139 0.88685791

115 Mar-05 1109.06 838.148648 97.6164217 132.3225901 1.3232259

116 Apr-05 1174.97 839.1947354 101.7102002 140.0116028 1.40011603

117 May-05 1095.68 840.2069226 103.8383672 130.4059715 1.30405972

118 Jun-05 934.69 841.186268 107.3118674 111.1156988 1.11115699

119 Jul-05 748.69 842.1337994 110.380944 88.90392483 0.88903925

120 Aug-05 757.4 843.050515 109.7244943 89.84040535 0.89840405

121 Sep-05 749.03 843.9373841 106.4237817 88.75421496 0.88754215

122 Oct-05 815.14 844.7953475 104.0159813 96.48964124 0.96489641

123 Nov-05 879.53 845.6253186 92.26314862 104.0094213 1.04009421

124 Dec-05 849.42 846.4281836 89.89484152 100.3534637 1.00353464


125 Jan-06 849.75 847.2048027 87.50457237 100.3004229 1.00300423

126 Feb-06 821.46 847.9560103 89.31537968 96.87530839 0.96875308

127 Mar-06 808.86 848.6826159 97.6164217 95.30771396 0.95307714

128 Apr-06 800.33 849.3854047 101.7102002 94.2246 0.942246

129 May-06 800.19 850.0651379 103.8383672 94.13278633 0.94132786

130 Jun-06 665.84 850.7225542 107.3118674 78.26758521 0.78267585

131 Jul-06 734.4 851.3583693 110.380944 86.26214606 0.86262146

132 Aug-06 830.84 851.9732773 109.7244943 97.5194906 0.97519491

133 Sep-06 878.63 852.567951 106.4237817 103.0568882 1.03056888

134 Oct-06 1036 853.1430426 104.0159813 121.4333293 1.21433329

135 Nov-06 931.12 853.699184 92.26314862 109.0688638 1.09068864

136 Dec-06 792.8 854.2369877 89.89484152 92.80796915 0.92807969


137 Jan-07 797.09 854.7570472 87.50457237 93.25339904 0.93253399

138 Feb-07 841.82 855.2599374 89.31537968 98.42855525 0.98428555

139 Mar-07 811.34 855.7462155 97.6164217 94.81081953 0.9481082

140 Apr-07 855.84 856.2164209 101.7102002 99.95603671 0.99956037

141 May-07 886.84 856.6710765 103.8383672 103.5216461 1.03521646

142 Jun-07 935.34 857.1106885 107.3118674 109.1270955 1.09127096

143 Jul-07 1142.48 857.5357472 110.380944 133.2282653 1.33228265

144 Aug-07 1231.13 857.9467274 109.7244943 143.4972546 1.43497255

145 Sep-07 1032.22 858.344089 106.4237817 120.2571339 1.20257134

146 Oct-07 974.51 858.728277 104.0159813 113.4829289 1.13482929

147 Nov-07 1045.7 859.0997226 92.26314862 121.7204444 1.21720444

148 Dec-07 925.87 859.4588431 89.89484152 107.7270898 1.0772709


149 Jan-08 1029.65 859.8060425 87.50457237 119.7537525 1.19753753

150 Feb-08 1049.03 860.1417119 89.31537968 121.9601358 1.21960136

151 Mar-08 1230.77 860.4662298 97.6164217 143.0352473 1.43035247

152 Apr-08 1233.72 860.7799627 101.7102002 143.325827 1.43325827

153 May-08 1317.69 861.0832653 103.8383672 153.027013 1.53027013

154 Jun-08 1414.43 861.3764807 107.3118674 164.2057836 1.64205784

155 Jul-08 1431.69 861.6599411 110.380944 166.1548752 1.66154875

156 Aug-08 1131.85 861.9339681 109.7244943 131.3151636 1.31315164

157 Sep-08 923.97 862.1988726 106.4237817 107.1643712 1.07164371

158 Oct-08 909.83 862.4549557 104.0159813 105.4930456 1.05493046

159 Nov-08 853.34 862.7025085 92.26314862 98.91474657 0.98914747

160 Dec-08 761.72 862.941813 89.89484152 88.2701462 0.88270146


161 Jan-09 782.89 863.1731418 87.50457237 90.6990686 0.90699069

162 Feb-09 766.46 863.3967585 89.31537968 88.77262886 0.88772629

163 Mar-09 847.05 863.6129185 97.6164217 98.08213633 0.98082136

164 Apr-09 904.52 863.8218685 101.7102002 104.7114032 1.04711403

165 May-09 888.24 864.0238474 103.8383672 102.8027181 1.02802718

166 Jun-09 816.12 864.2190862 107.3118674 94.43438741 0.94434387

167 Jul-09 715.36 864.4078084 110.380944 82.75723484 0.82757235

168 Aug-09 836.29 864.5902301 109.7244943 96.72674648 0.96726747

169 Sep-09 1030.95 864.7665604 106.4237817 119.2171445 1.19217145

170 Oct-09 1152.61 864.9370015 104.0159813 133.2594164 1.33259416

171 Nov-09 1154.41 865.101749 92.26314862 133.4421068 1.33442107

172 Dec-09 1013.58 865.260992 89.89484152 117.1415341 1.17141534


173 Jan-10 1089.26 865.4149135 87.50457237 125.8656377 1.25865638

174 Feb-10 981.59 865.5636904 89.31537968 113.4047108 1.13404711

175 Mar-10 954.72 865.7074938 97.6164217 110.2820533 1.10282053

176 Apr-10 994.73 865.8464893 101.7102002 114.8852611 1.14885261

177 May-10 1054.71 865.9808367 103.8383672 121.7936882 1.21793688

178 Jun-10 1201.27 866.1106909 107.3118674 138.6970525 1.38697053

179 Jul-10 1302.41 866.2362014 110.380944 150.3527557 1.50352756

180 Aug-10 1139.33 866.357513 109.7244943 131.5080648 1.31508065

181 Sep-10 1046.85 866.4747657 106.4237817 120.8171365 1.20817137

182 Oct-10 1086.32 866.5880945 104.0159813 125.3559802 1.2535598

183 Nov-10 823.35 866.6976305 92.26314862 94.99852901 0.94998529

184 Dec-10 723.89 866.8035001 89.89484152 83.51258387 0.83512584


185 Jan-11 734.61 866.9058255 87.50457237 84.73930829 0.84739308

186 Feb-11 884.96 867.004725 89.31537968 102.0709547 1.02070955

187 Mar-11 852.44 867.100313 97.6164217 98.3092714 0.98309271

188 Apr-11 880.97 867.1926999 101.7102002 101.5887242 1.01588724

189 May-11 836.41 867.2819927 103.8383672 96.4403743 0.96440374

190 Jun-11 916.4 867.3682947 107.3118674 105.652928 1.05652928

191 Jul-11 971.56 867.4517057 110.380944 112.0016242 1.12001624

192 Aug-11 948.83 867.5323224 109.7244943 109.3711411 1.09371141

193 Sep-11 1194.94 867.6102381 106.4237817 137.7277431 1.37727743

194 Oct-11 1032.7 867.685543 104.0159813 119.0177719 1.19017772

195 Nov-11 681.65 867.7583245 92.26314862 78.55297734 0.78552977

196 Dec-11 757.73 867.8286669 89.89484152 87.31331758 0.87313318


197 Jan-12 730.58 867.8966517 87.50457237 84.17822544 0.84178225

198 Feb-12 778.64 867.9623578 89.31537968 89.7089595 0.8970896

199 Mar-12 802.57 868.0258614 97.6164217 92.45922682 0.92459227

200 Apr-12 822.89 868.0872361 101.7102002 94.79346841 0.94793468

201 May-12 755.83 868.1465533 103.8383672 87.06248929 0.87062489

202 Jun-12 952.76 868.2038817 107.3118674 109.7392007 1.09739201

203 Jul-12 1015.16 868.2592879 110.380944 116.9189912 1.16918991

204 Aug-12 970.39 868.3128362 109.7244943 111.755805 1.11755805

205 Sep-12 1000.89 868.3645889 106.4237817 115.2614942 1.15261494

206 Oct-12 980.85 868.4146059 104.0159813 112.9472021 1.12947202

207 Nov-12 846.84 868.4629456 92.26314862 97.51020517 0.97510205

208 Dec-12 758.09 868.5096639 89.89484152 87.28630567 0.87286306


209 Jan-13 750.03 868.5548152 87.50457237 86.35378987 0.8635379

210 Feb-13 819.58 868.598452 89.31537968 94.3566038 0.94356604

211 Mar-13 908.1 868.6406251 97.6164217 104.5426582 1.04542658

212 Apr-13 980.49 868.6813833 101.7102002 112.8710732 1.12871073

213 May-13 1057.01 868.7207743 103.8383672 121.6743091 1.21674309

214 Jun-13 1157.65 868.7588436 107.3118674 133.2533198 1.3325332

215 Jul-13 1121.23 868.7956358 110.380944 129.0556667 1.29055667

216 Aug-13 1190.81 868.8311934 109.7244943 137.0588451 1.37058845

217 Sep-13 1119.72 868.865558 106.4237817 128.8714911 1.28871491

218 Oct-13 997.26 868.8987695 104.0159813 114.7728637 1.14772864

219 Nov-13 766 868.9308665 92.26314862 88.15430888 0.88154309

220 Dec-13 739.98 868.9618865 89.89484152 85.15678438 0.85156784


221 Jan-14 753.15 868.9918654 87.50457237 86.66939588 0.86669396

222 Feb-14 770.93 869.0208383 89.31537968 88.71248721 0.88712487

223 Mar-14 808.11 869.0488388 97.6164217 92.98786948 0.9298787

224 Apr-14 846.89 869.0758996 101.7102002 97.44718504 0.97447185

225 May-14 834.98 869.1020521 103.8383672 96.07387279 0.96073873

226 Jun-14 834.56 869.1273269 107.3118674 96.02275457 0.96022755

227 Jul-14 783.04 869.1517533 110.380944 90.09243749 0.90092438

228 Aug-14 768.17 869.1753598 109.7244943 88.37917359 0.88379174

229 Sep-14 771.03 869.1981739 106.4237817 88.70589276 0.88705893

230 Oct-14 732.15 869.2202222 104.0159813 84.23066805 0.84230668

231 Nov-14 717.87 869.2415304 92.26314862 82.58579174 0.82585792

232 Dec-14 769.23 869.2621233 89.89484152 88.49229471 0.88492295


233 Jan-15 758.02 869.2820249 87.50457237 87.20069877 0.87200699

234 Feb-15 704.17 869.3012584 89.31537968 81.00413904 0.81004139

235 Mar-15 633.29 869.3198462 97.6164217 72.84890628 0.72848906

236 Apr-15 612.13 869.3378099 101.7102002 70.4133644 0.70413364

237 May-15 608.64 869.3551706 103.8383672 70.01051131 0.70010511

238 Jun-15 629.9 869.3719484 107.3118674 72.45460372 0.72454604

239 Jul-15 640.11 869.3881629 110.380944 73.62764152 0.73627642

240 Aug-15 684.28 869.403833 109.7244943 78.70680736 0.78706807

241 Sep-15 631.91 869.4189769 106.4237817 72.68187339 0.72681873

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 2390

0.5

1

1.5

2

2.5

3

3.5

4

4.5Residuals

Residuals

Residuals after seasonal component is

eliminated

t Months yt Trend Values Seasonal Indices yt/st*100 Residuals

1 Sep-95 537.55 140.1202958 106.4237817 505.1032689 5.051032689

2 Oct-95 546.21 148.9834567 104.0159813 525.1212296 5.251212296

3 Nov-95 564.24 158.0812077 92.26314862 611.55511 6.1155511

4 Dec-95 443.23 167.4008658 89.89484152 493.0538755 4.930538755


5 Jan-96 417.53 176.9291779 87.50457237 477.152209 4.77152209

6 Feb-96 434.47 186.6524081 89.31537968 486.4447775 4.864447775

7 Mar-96 474.39 196.5564243 97.6164217 485.9735603 4.859735603

8 Apr-96 528.79 206.6267836 101.7102002 519.8986915 5.198986915

9 May-96 520.09 216.8488146 103.8383672 500.8649633 5.008649633

10 Jun-96 559.05 227.2076975 107.3118674 520.9582256 5.209582256

11 Jul-96 527.45 237.6885408 110.380944 477.8451612 4.778451612

12 Aug-96 527.25 248.2764534 109.7244943 480.5216951 4.805216951

13 Sep-96 528.42 258.9566136 106.4237817 496.5243593 4.965243593

14 Oct-96 473.7 269.7143327 104.0159813 455.4107879 4.554107879

15 Nov-96 474.99 280.5351144 92.26314862 514.8209303 5.148209303

16 Dec-96 433.88 291.4047095 89.89484152 482.6528337 4.826528337


17 Jan-97 424.6 302.3091651 87.50457237 485.2317868 4.852317868

18 Feb-97 406.73 313.2348696 89.31537968 455.3862968 4.553862968

19 Mar-97 419.62 324.1685924 97.6164217 429.8661974 4.298661974

20 Apr-97 451.19 335.0975192 101.7102002 443.6034921 4.436034921

21 May-97 470.14 346.009282 103.8383672 452.7613564 4.527613564

22 Jun-97 439.75 356.8919852 107.3118674 409.7869237 4.097869237

23 Jul-97 515.5 367.7342273 110.380944 467.0190172 4.670190172

24 Aug-97 571.51 378.525118 109.7244943 520.8590877 5.208590877

25 Sep-97 547.13 389.2542916 106.4237817 514.1050163 5.141050163

26 Oct-97 493.47 399.9119175 104.0159813 474.4174826 4.744174826

27 Nov-97 414.98 410.4887057 92.26314862 449.7787104 4.497787104

28 Dec-97 352.94 420.9759105 89.89484152 392.6142969 3.926142969


29 Jan-98 361.63 431.3653306 87.50457237 413.2698329 4.132698329

30 Feb-98 394.7 441.6493067 89.31537968 441.917172 4.41917172

31 Mar-98 408.36 451.8207166 97.6164217 418.331253 4.18331253

32 Apr-98 443.83 461.8729679 101.7102002 436.3672464 4.363672464

33 May-98 448.75 471.7999893 103.8383672 432.1620341 4.321620341

34 Jun-98 457.59 481.5962196 107.3118674 426.4113665 4.264113665

35 Jul-98 542.93 491.2565955 110.380944 491.869321 4.91869321

36 Aug-98 506.8 500.7765377 109.7244943 461.8841064 4.618841064

37 Sep-98 499.06 510.1519365 106.4237817 468.9365405 4.689365405

38 Oct-98 433 519.379136 104.0159813 416.2821853 4.162821853

39 Nov-98 428.24 528.4549176 92.26314862 464.1506456 4.641506456

40 Dec-98 383.92 537.3764829 89.89484152 427.076786 4.27076786


41 Jan-99 417.37 546.1414366 87.50457237 476.9693614 4.769693614

42 Feb-99 403.97 554.7477682 89.31537968 452.2961235 4.522961235

43 Mar-99 439.64 563.1938342 97.6164217 450.3750418 4.503750418

44 Apr-99 447.14 571.4783401 101.7102002 439.6215906 4.396215906

45 May-99 444.25 579.6003222 103.8383672 427.8283758 4.278283758

46 Jun-99 484.44 587.5591296 107.3118674 451.4318984 4.514318984

47 Jul-99 460.27 595.3544067 110.380944 416.9832066 4.169832066

48 Aug-99 492.36 602.9860755 109.7244943 448.7238726 4.487238726

49 Sep-99 471.85 610.4543182 106.4237817 443.3689469 4.433689469

50 Oct-99 517.99 617.7595608 104.0159813 497.9907833 4.979907833

51 Nov-99 340.37 624.9024566 92.26314862 368.9121877 3.689121877

52 Dec-99 339.07 631.8838701 89.89484152 377.185158 3.77185158


53 Jan-00 348.9 638.7048617 87.50457237 398.7220217 3.987220217

54 Feb-00 323.59 645.3666728 89.31537968 362.3004248 3.623004248

55 Mar-00 299.18 651.8707115 97.6164217 306.4853175 3.064853175

56 Apr-00 337.49 658.2185387 101.7102002 331.8152941 3.318152941

57 May-00 411.02 664.4118547 103.8383672 395.826717 3.95826717

58 Jun-00 426.49 670.4524869 107.3118674 397.4304152 3.974304152

59 Jul-00 401.78 676.3423773 110.380944 363.9939878 3.639939878

60 Aug-00 392.32 682.0835712 109.7244943 357.5500643 3.575500643

61 Sep-00 364.71 687.6782064 106.4237817 342.6959598 3.426959598

62 Oct-00 379.84 693.1285024 104.0159813 365.1746542 3.651746542

63 Nov-00 364.21 698.4367507 92.26314862 394.7513232 3.947513232

64 Dec-00 309.02 703.6053056 89.89484152 343.7572109 3.437572109


65 Jan-01 348.93 708.6365756 87.50457237 398.7563056 3.987563056

66 Feb-01 407.17 713.5330147 89.31537968 455.8789331 4.558789331

67 Mar-01 554.81 718.2971148 97.6164217 568.3572398 5.683572398

68 Apr-01 629.72 722.9313988 101.7102002 619.1316099 6.191316099

69 May-01 734.34 727.4384133 103.8383672 707.1952492 7.071952492

70 Jun-01 830.56 731.8207226 107.3118674 773.9684533 7.739684533

71 Jul-01 962.94 736.0809025 110.380944 872.3788407 8.723788407

72 Aug-01 784.58 740.2215354 109.7244943 715.0454463 7.150454463

73 Sep-01 577.54 744.2452043 106.4237817 542.6794566 5.426794566

74 Oct-01 423.63 748.154489 104.0159813 407.2739542 4.072739542

75 Nov-01 466 751.9519611 92.26314862 505.0770616 5.050770616

76 Dec-01 425.76 755.6401805 89.89484152 473.6200574 4.736200574


77 Jan-02 443.71 759.2216915 87.50457237 507.0706456 5.070706456

78 Feb-02 454.62 762.6990193 89.31537968 509.0052818 5.090052818

79 Mar-02 590.33 766.0746674 97.6164217 604.7445601 6.047445601

80 Apr-02 579.16 769.3511144 101.7102002 569.4217481 5.694217481

81 May-02 635.51 772.5308118 103.8383672 612.018483 6.12018483

82 Jun-02 635.47 775.6161815 107.3118674 592.1712255 5.921712255

83 Jul-02 653.47 778.6096141 110.380944 592.0134183 5.920134183

84 Aug-02 637.6 781.5134667 109.7244943 581.0917645 5.810917645

85 Sep-02 626.68 784.3300617 106.4237817 588.8533467 5.888533467

86 Oct-02 614.28 787.0616853 104.0159813 590.5630965 5.905630965

87 Nov-02 476.8 789.7105861 92.26314862 516.7827103 5.167827103

88 Dec-02 426.76 792.2789743 89.89484152 474.7324683 4.747324683


89 Jan-03 547.13 794.7690208 87.50457237 625.2587553 6.252587553

90 Feb-03 505.06 797.1828562 89.31537968 565.4793181 5.654793181

91 Mar-03 633.16 799.5225706 97.6164217 648.6203745 6.486203745

92 Apr-03 700 801.7902129 101.7102002 688.229891 6.88229891

93 May-03 685 803.9877904 103.8383672 659.6790938 6.596790938

94 Jun-03 719.44 806.1172688 107.3118674 670.4197939 6.704197939

95 Jul-03 749.65 808.1805719 110.380944 679.1480237 6.791480237

96 Aug-03 793.2 810.1795813 109.7244943 722.9014861 7.229014861

97 Sep-03 782.99 812.1161371 106.4237817 735.7284132 7.357284132

98 Oct-03 836.15 813.9920374 104.0159813 803.8668574 8.038668574

99 Nov-03 660.98 815.8090387 92.26314862 716.4073738 7.164073738

100 Dec-03 582.95 817.5688562 89.89484152 648.479924 6.48479924


101 Jan-04 718.27 819.273164 87.50457237 820.8371066 8.208371066

102 Feb-04 831.05 820.9235957 89.31537968 930.4668501 9.304668501

103 Mar-04 934.72 822.5217443 97.6164217 957.5438064 9.575438064

104 Apr-04 858.92 824.0691634 101.7102002 844.4777399 8.444777399

105 May-04 872.75 825.5673668 103.8383672 840.4889476 8.404889476

106 Jun-04 920.82 827.01783 107.3118674 858.0784425 8.580784425

107 Jul-04 994.18 828.4219899 110.380944 900.6808273 9.006808273

108 Aug-04 935.59 829.7812459 109.7244943 852.6719635 8.526719635

109 Sep-04 901.3 831.0969601 106.4237817 846.8971747 8.468971747

110 Oct-04 921.2 832.3704586 104.0159813 885.6331388 8.856331388

111 Nov-04 715.34 833.6030312 92.26314862 775.3258053 7.753258053

112 Dec-04 686.13 834.7959328 89.89484152 763.2584789 7.632584789


113 Jan-05 640.12 835.950384 87.50457237 731.5274879 7.315274879

114 Feb-05 742.36 837.0675712 89.31537968 831.1670427 8.311670427

115 Mar-05 1109.06 838.148648 97.6164217 1136.140806 11.36140806

116 Apr-05 1174.97 839.1947354 101.7102002 1155.213536 11.55213536

117 May-05 1095.68 840.2069226 103.8383672 1055.178379 10.55178379

118 Jun-05 934.69 841.186268 107.3118674 871.0033876 8.710033876

119 Jul-05 748.69 842.1337994 110.380944 678.2783084 6.782783084

120 Aug-05 757.4 843.050515 109.7244943 690.2743137 6.902743137

121 Sep-05 749.03 843.9373841 106.4237817 703.8182522 7.038182522

122 Oct-05 815.14 844.7953475 104.0159813 783.6680382 7.836680382

123 Nov-05 879.53 845.6253186 92.26314862 953.2841803 9.532841803

124 Dec-05 849.42 846.4281836 89.89484152 944.9040519 9.449040519


125 Jan-06 849.75 847.2048027 87.50457237 971.0921121 9.710921121

126 Feb-06 821.46 847.9560103 89.31537968 919.7296176 9.197296176

127 Mar-06 808.86 848.6826159 97.6164217 828.610582 8.28610582

128 Apr-06 800.33 849.3854047 101.7102002 786.872898 7.86872898

129 May-06 800.19 850.0651379 103.8383672 770.6111154 7.706111154

130 Jun-06 665.84 850.7225542 107.3118674 620.4719165 6.204719165

131 Jul-06 734.4 851.3583693 110.380944 665.3322332 6.653322332

132 Aug-06 830.84 851.9732773 109.7244943 757.2055859 7.572055859

133 Sep-06 878.63 852.567951 106.4237817 825.5955449 8.255955449

134 Oct-06 1036 853.1430426 104.0159813 996.0007944 9.960007944

135 Nov-06 931.12 853.699184 92.26314862 1009.20033 10.0920033

136 Dec-06 792.8 854.2369877 89.89484152 881.9193477 8.819193477


137 Jan-07 797.09 854.7570472 87.50457237 910.9123997 9.109123997

138 Feb-07 841.82 855.2599374 89.31537968 942.5252437 9.425252437

139 Mar-07 811.34 855.7462155 97.6164217 831.1511381 8.311511381

140 Apr-07 855.84 856.2164209 101.7102002 841.4495284 8.414495284

141 May-07 886.84 856.6710765 103.8383672 854.0581132 8.540581132

142 Jun-07 935.34 857.1106885 107.3118674 871.6090988 8.716090988

143 Jul-07 1142.48 857.5357472 110.380944 1035.033728 10.35033728

144 Aug-07 1231.13 857.9467274 109.7244943 1122.019297 11.22019297

145 Sep-07 1032.22 858.344089 106.4237817 969.9147916 9.699147916

146 Oct-07 974.51 858.728277 104.0159813 936.8848785 9.368848785

147 Nov-07 1045.7 859.0997226 92.26314862 1133.388591 11.33388591

148 Dec-07 925.87 859.4588431 89.89484152 1029.947864 10.29947864


149 Jan-08 1029.65 859.8060425 87.50457237 1176.681369 11.76681369

150 Feb-08 1049.03 860.1417119 89.31537968 1174.523362 11.74523362

151 Mar-08 1230.77 860.4662298 97.6164217 1260.822696 12.60822696

152 Apr-08 1233.72 860.7799627 101.7102002 1212.975687 12.12975687

153 May-08 1317.69 861.0832653 103.8383672 1268.981818 12.68981818

154 Jun-08 1414.43 861.3764807 107.3118674 1318.055528 13.18055528

155 Jul-08 1431.69 861.6599411 110.380944 1297.044533 12.97044533

156 Aug-08 1131.85 861.9339681 109.7244943 1031.538133 10.31538133

157 Sep-08 923.97 862.1988726 106.4237817 868.1988045 8.681988045

158 Oct-08 909.83 862.4549557 104.0159813 874.7021262 8.747021262

159 Nov-08 853.34 862.7025085 92.26314862 924.8979823 9.248979823

160 Dec-08 761.72 862.941813 89.89484152 847.3456175 8.473456175


161 Jan-09 782.89 863.1731418 87.50457237 894.6846763 8.946846763

162 Feb-09 766.46 863.3967585 89.31537968 858.1500776 8.581500776

163 Mar-09 847.05 863.6129185 97.6164217 867.7330978 8.677330978

164 Apr-09 904.52 863.8218685 101.7102002 889.3110014 8.893110014

165 May-09 888.24 864.0238474 103.8383672 855.4063624 8.554063624

166 Jun-09 816.12 864.2190862 107.3118674 760.512346 7.60512346

167 Jul-09 715.36 864.4078084 110.380944 648.082879 6.48082879

168 Aug-09 836.29 864.5902301 109.7244943 762.1725717 7.621725717

169 Sep-09 1030.95 864.7665604 106.4237817 968.7214493 9.687214493

170 Oct-09 1152.61 864.9370015 104.0159813 1108.108567 11.08108567

171 Nov-09 1154.41 865.101749 92.26314862 1251.214615 12.51214615

172 Dec-09 1013.58 865.260992 89.89484152 1127.517422 11.27517422


173 Jan-10 1089.26 865.4149135 87.50457237 1244.803523 12.44803523

174 Feb-10 981.59 865.5636904 89.31537968 1099.015649 10.99015649

175 Mar-10 954.72 865.7074938 97.6164217 978.0321624 9.780321624

176 Apr-10 994.73 865.8464893 101.7102002 978.0041706 9.780041706

177 May-10 1054.71 865.9808367 103.8383672 1015.722828 10.15722828

178 Jun-10 1201.27 866.1106909 107.3118674 1119.419529 11.19419529

179 Jul-10 1302.41 866.2362014 110.380944 1179.922867 11.79922867

180 Aug-10 1139.33 866.357513 109.7244943 1038.355207 10.38355207

181 Sep-10 1046.85 866.4747657 106.4237817 983.661719 9.83661719

182 Oct-10 1086.32 866.5880945 104.0159813 1044.377976 10.44377976

183 Nov-10 823.35 866.6976305 92.26314862 892.3931302 8.923931302

184 Dec-10 723.89 866.8035001 89.89484152 805.2631138 8.052631138


185 Jan-11 734.61 866.9058255 87.50457237 839.5104166 8.395104166

186 Feb-11 884.96 867.004725 89.31537968 990.8259957 9.908259957

187 Mar-11 852.44 867.100313 97.6164217 873.2547097 8.732547097

188 Apr-11 880.97 867.1926999 101.7102002 866.1569815 8.661569815

189 May-11 836.41 867.2819927 103.8383672 805.4922494 8.054922494

190 Jun-11 916.4 867.3682947 107.3118674 853.9596063 8.539596063

191 Jul-11 971.56 867.4517057 110.380944 880.1881597 8.801881597

192 Aug-11 948.83 867.5323224 109.7244943 864.738549 8.64738549

193 Sep-11 1194.94 867.6102381 106.4237817 1122.812948 11.22812948

194 Oct-11 1032.7 867.685543 104.0159813 992.828205 9.92828205

195 Nov-11 681.65 867.7583245 92.26314862 738.8106847 7.388106847

196 Dec-11 757.73 867.8286669 89.89484152 842.9070981 8.429070981


197 Jan-12 730.58 867.8966517 87.50457237 834.9049429 8.349049429

198 Feb-12 778.64 867.9623578 89.31537968 871.7871466 8.717871466

199 Mar-12 802.57 868.0258614 97.6164217 822.166994 8.22166994

200 Apr-12 822.89 868.0872361 101.7102002 809.0535642 8.090535642

201 May-12 755.83 868.1465533 103.8383672 727.8908751 7.278908751

202 Jun-12 952.76 868.2038817 107.3118674 887.842159 8.87842159

203 Jul-12 1015.16 868.2592879 110.380944 919.6877312 9.196877312

204 Aug-12 970.39 868.3128362 109.7244943 884.3877624 8.843877624

205 Sep-12 1000.89 868.3645889 106.4237817 940.4758828 9.404758828

206 Oct-12 980.85 868.4146059 104.0159813 942.9800957 9.429800957

207 Nov-12 846.84 868.4629456 92.26314862 917.852916 9.17852916

208 Dec-12 758.09 868.5096639 89.89484152 843.307566 8.43307566


209 Jan-13 750.03 868.5548152 87.50457237 857.1323529 8.571323529

210 Feb-13 819.58 868.598452 89.31537968 917.624717 9.17624717

211 Mar-13 908.1 868.6406251 97.6164217 930.2738045 9.302738045

212 Apr-13 980.49 868.6813833 101.7102002 964.0036083 9.640036083

213 May-13 1057.01 868.7207743 103.8383672 1017.937809 10.17937809

214 Jun-13 1157.65 868.7588436 107.3118674 1078.771648 10.78771648

215 Jul-13 1121.23 868.7956358 110.380944 1015.782217 10.15782217

216 Aug-13 1190.81 868.8311934 109.7244943 1085.272716 10.85272716

217 Sep-13 1119.72 868.865558 106.4237817 1052.133257 10.52133257

218 Oct-13 997.26 868.8987695 104.0159813 958.7565176 9.587565176

219 Nov-13 766 868.9308665 92.26314862 830.2339683 8.302339683

220 Dec-13 739.98 868.9618865 89.89484152 823.1618049 8.231618049


221 Jan-14 753.15 868.9918654 87.50457237 860.6978808 8.606978808

222 Feb-14 770.93 869.0208383 89.31537968 863.1548147 8.631548147

223 Mar-14 808.11 869.0488388 97.6164217 827.8422686 8.278422686

224 Apr-14 846.89 869.0758996 101.7102002 832.6500176 8.326500176

225 May-14 834.98 869.1020521 103.8383672 804.1151091 8.041151091

226 Jun-14 834.56 869.1273269 107.3118674 777.6959069 7.776959069

227 Jul-14 783.04 869.1517533 110.380944 709.3978103 7.093978103

228 Aug-14 768.17 869.1753598 109.7244943 700.0898066 7.000898066

229 Sep-14 771.03 869.1981739 106.4237817 724.4903235 7.244903235

230 Oct-14 732.15 869.2202222 104.0159813 703.8822216 7.038822216

231 Nov-14 717.87 869.2415304 92.26314862 778.0679619 7.780679619

232 Dec-14 769.23 869.2621233 89.89484152 855.6998232 8.556998232


233 Jan-15 758.02 869.2820249 87.50457237 866.2633043 8.662633043

234 Feb-15 704.17 869.3012584 89.31537968 788.4084494 7.884084494

235 Mar-15 633.29 869.3198462 97.6164217 648.7535488 6.487535488

236 Apr-15 612.13 869.3378099 101.7102002 601.8373759 6.018373759

237 May-15 608.64 869.3551706 103.8383672 586.1417279 5.861417279

238 Jun-15 629.9 869.3719484 107.3118674 586.9807464 5.869807464

239 Jul-15 640.11 869.3881629 110.380944 579.9098799 5.799098799

240 Aug-15 684.28 869.403833 109.7244943 623.634681 6.23634681

241 Sep-15 631.91 869.4189769 106.4237817 593.7676619 5.937676619

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 2390

2

4

6

8

10

12

14 Residuals

Residuals

RESIDUALS AFTER TREND AND SEASONAL COMPONENT IS

ELIMINATED

t Months yt Trend Values Seasonal Indices yt*100/(Tt*st) Residuals

1 Sep-95 537.55 140.1202958 106.4237817 3.604783062 0.036047831

2 Oct-95 546.21 148.9834567 104.0159813 3.524694897 0.035246949

3 Nov-95 564.24 158.0812077 92.26314862 3.868613599 0.038686136

4 Dec-95 443.23 167.4008658 89.89484152 2.945348419 0.029453484


5 Jan-96 417.53 176.9291779 87.50457237 2.69685427 0.026968543

6 Feb-96 434.47 186.6524081 89.31537968 2.606153237 0.026061532

7 Mar-96 474.39 196.5564243 97.6164217 2.472437937 0.024724379

8 Apr-96 528.79 206.6267836 101.7102002 2.516124398 0.025161244

9 May-96 520.09 216.8488146 103.8383672 2.309742686 0.023097427

10 Jun-96 559.05 227.2076975 107.3118674 2.292872254 0.022928723

11 Jul-96 527.45 237.6885408 110.380944 2.010383671 0.020103837

12 Aug-96 527.25 248.2764534 109.7244943 1.935429996 0.0193543

13 Sep-96 528.42 258.9566136 106.4237817 1.917403663 0.019174037

14 Oct-96 473.7 269.7143327 104.0159813 1.688493094 0.016884931

15 Nov-96 474.99 280.5351144 92.26314862 1.835139003 0.01835139

16 Dec-96 433.88 291.4047095 89.89484152 1.656297301 0.016562973


17 Jan-97 424.6 302.3091651 87.50457237 1.605084605 0.016050846

18 Feb-97 406.73 313.2348696 89.31537968 1.453817378 0.014538174

19 Mar-97 419.62 324.1685924 97.6164217 1.326057513 0.013260575

20 Apr-97 451.19 335.0975192 101.7102002 1.323804167 0.013238042

21 May-97 470.14 346.009282 103.8383672 1.30852373 0.013085237

22 Jun-97 439.75 356.8919852 107.3118674 1.148209937 0.011482099

23 Jul-97 515.5 367.7342273 110.380944 1.269990614 0.012699906

24 Aug-97 571.51 378.525118 109.7244943 1.376022523 0.013760225

25 Sep-97 547.13 389.2542916 106.4237817 1.320743348 0.013207433

26 Oct-97 493.47 399.9119175 104.0159813 1.186304938 0.011863049

27 Nov-97 414.98 410.4887057 92.26314862 1.09571519 0.010957152

28 Dec-97 352.94 420.9759105 89.89484152 0.932628892 0.009326289


29 Jan-98 361.63 431.3653306 87.50457237 0.958050644 0.009580506

30 Feb-98 394.7 441.6493067 89.31537968 1.000606511 0.010006065

31 Mar-98 408.36 451.8207166 97.6164217 0.925878867 0.009258789

32 Apr-98 443.83 461.8729679 101.7102002 0.944777627 0.009447776

33 May-98 448.75 471.7999893 103.8383672 0.91598568 0.009159857

34 Jun-98 457.59 481.5962196 107.3118674 0.885412611 0.008854126

35 Jul-98 542.93 491.2565955 110.380944 1.001247262 0.010012473

36 Aug-98 506.8 500.7765377 109.7244943 0.922335756 0.009223358

37 Sep-98 499.06 510.1519365 106.4237817 0.919209567 0.009192096

38 Oct-98 433 519.379136 104.0159813 0.80149963 0.008014996

39 Nov-98 428.24 528.4549176 92.26314862 0.878316447 0.008783164

40 Dec-98 383.92 537.3764829 89.89484152 0.794744094 0.007947441


41 Jan-99 417.37 546.1414366 87.50457237 0.873344027 0.00873344

42 Feb-99 403.97 554.7477682 89.31537968 0.815318509 0.008153185

43 Mar-99 439.64 563.1938342 97.6164217 0.799680349 0.007996803

44 Apr-99 447.14 571.4783401 101.7102002 0.769270784 0.007692708

45 May-99 444.25 579.6003222 103.8383672 0.738143785 0.007381438

46 Jun-99 484.44 587.5591296 107.3118674 0.768317392 0.007683174

47 Jul-99 460.27 595.3544067 110.380944 0.700394928 0.007003949

48 Aug-99 492.36 602.9860755 109.7244943 0.744169544 0.007441695

49 Sep-99 471.85 610.4543182 106.4237817 0.726293408 0.007262934

50 Oct-99 517.99 617.7595608 104.0159813 0.80612396 0.00806124

51 Nov-99 340.37 624.9024566 92.26314862 0.590351636 0.005903516

52 Dec-99 339.07 631.8838701 89.89484152 0.596921643 0.005969216


53 Jan-00 348.9 638.7048617 87.50457237 0.624266458 0.006242665

54 Feb-00 323.59 645.3666728 89.31537968 0.561386945 0.005613869

55 Mar-00 299.18 651.8707115 97.6164217 0.470162736 0.004701627

56 Apr-00 337.49 658.2185387 101.7102002 0.504111134 0.005041111

57 May-00 411.02 664.4118547 103.8383672 0.595755049 0.00595755

58 Jun-00 426.49 670.4524869 107.3118674 0.592779389 0.005927794

59 Jul-00 401.78 676.3423773 110.380944 0.53818007 0.005381801

60 Aug-00 392.32 682.0835712 109.7244943 0.524202722 0.005242027

61 Sep-00 364.71 687.6782064 106.4237817 0.498337677 0.004983377

62 Oct-00 379.84 693.1285024 104.0159813 0.52684986 0.005268499

63 Nov-00 364.21 698.4367507 92.26314862 0.565192658 0.005651927

64 Dec-00 309.02 703.6053056 89.89484152 0.488565405 0.004885654


65 Jan-01 348.93 708.6365756 87.50457237 0.562709179 0.005627092

66 Feb-01 407.17 713.5330147 89.31537968 0.63890377 0.006389038

67 Mar-01 554.81 718.2971148 97.6164217 0.79125647 0.007912565

68 Apr-01 629.72 722.9313988 101.7102002 0.856418204 0.008564182

69 May-01 734.34 727.4384133 103.8383672 0.972171989 0.00972172

70 Jun-01 830.56 731.8207226 107.3118674 1.057592973 0.01057593

71 Jul-01 962.94 736.0809025 110.380944 1.185167062 0.011851671

72 Aug-01 784.58 740.2215354 109.7244943 0.96598844 0.009659884

73 Sep-01 577.54 744.2452043 106.4237817 0.729167556 0.007291676

74 Oct-01 423.63 748.154489 104.0159813 0.544371464 0.005443715

75 Nov-01 466 751.9519611 92.26314862 0.671687937 0.006716879

76 Dec-01 425.76 755.6401805 89.89484152 0.626779874 0.006267799


77 Jan-02 443.71 759.2216915 87.50457237 0.667882189 0.006678822

78 Feb-02 454.62 762.6990193 89.31537968 0.66737372 0.006673737

79 Mar-02 590.33 766.0746674 97.6164217 0.789406811 0.007894068

80 Apr-02 579.16 769.3511144 101.7102002 0.74013248 0.007401325

81 May-02 635.51 772.5308118 103.8383672 0.792225337 0.007922253

82 Jun-02 635.47 775.6161815 107.3118674 0.763484878 0.007634849

83 Jul-02 653.47 778.6096141 110.380944 0.760346915 0.007603469

84 Aug-02 637.6 781.5134667 109.7244943 0.743546707 0.007435467

85 Sep-02 626.68 784.3300617 106.4237817 0.750772379 0.007507724

86 Oct-02 614.28 787.0616853 104.0159813 0.750339024 0.00750339

87 Nov-02 476.8 789.7105861 92.26314862 0.654395065 0.006543951

88 Dec-02 426.76 792.2789743 89.89484152 0.59919862 0.005991986


89 Jan-03 547.13 794.7690208 87.50457237 0.786717573 0.007867176

90 Feb-03 505.06 797.1828562 89.31537968 0.709347064 0.007093471

91 Mar-03 633.16 799.5225706 97.6164217 0.811259617 0.008112596

92 Apr-03 700 801.7902129 101.7102002 0.85836654 0.008583665

93 May-03 685 803.9877904 103.8383672 0.820508846 0.008205088

94 Jun-03 719.44 806.1172688 107.3118674 0.831665342 0.008316653

95 Jul-03 749.65 808.1805719 110.380944 0.840341933 0.008403419

96 Aug-03 793.2 810.1795813 109.7244943 0.892273149 0.008922731

97 Sep-03 782.99 812.1161371 106.4237817 0.905939901 0.009059399

98 Oct-03 836.15 813.9920374 104.0159813 0.987561082 0.009875611

99 Nov-03 660.98 815.8090387 92.26314862 0.87815572 0.008781557

100 Dec-03 582.95 817.5688562 89.89484152 0.793180806 0.007931808


101 Jan-04 718.27 819.273164 87.50457237 1.001908939 0.010019089

102 Feb-04 831.05 820.9235957 89.31537968 1.133439038 0.01133439

103 Mar-04 934.72 822.5217443 97.6164217 1.164156222 0.011641562

104 Apr-04 858.92 824.0691634 101.7102002 1.024765611 0.010247656

105 May-04 872.75 825.5673668 103.8383672 1.018074334 0.010180743

106 Jun-04 920.82 827.01783 107.3118674 1.037557367 0.010375574

107 Jul-04 994.18 828.4219899 110.380944 1.087224673 0.010872247

108 Aug-04 935.59 829.7812459 109.7244943 1.027586448 0.010275864

109 Sep-04 901.3 831.0969601 106.4237817 1.019011277 0.010190113

110 Oct-04 921.2 832.3704586 104.0159813 1.063989153 0.010639892

111 Nov-04 715.34 833.6030312 92.26314862 0.930089954 0.0093009

112 Dec-04 686.13 834.7959328 89.89484152 0.914305459 0.009143055


113 Jan-05 640.12 835.950384 87.50457237 0.875084816 0.008750848

114 Feb-05 742.36 837.0675712 89.31537968 0.992950953 0.00992951

115 Mar-05 1109.06 838.148648 97.6164217 1.355536167 0.013555362

116 Apr-05 1174.97 839.1947354 101.7102002 1.376573859 0.013765739

117 May-05 1095.68 840.2069226 103.8383672 1.255855374 0.012558554

118 Jun-05 934.69 841.186268 107.3118674 1.035446513 0.010354465

119 Jul-05 748.69 842.1337994 110.380944 0.805428198 0.008054282

120 Aug-05 757.4 843.050515 109.7244943 0.818781676 0.008187817

121 Sep-05 749.03 843.9373841 106.4237817 0.833969754 0.008339698

122 Oct-05 815.14 844.7953475 104.0159813 0.927642465 0.009276425

123 Nov-05 879.53 845.6253186 92.26314862 1.127312723 0.011273127

124 Dec-05 849.42 846.4281836 89.89484152 1.116342851 0.011163429


125 Jan-06 849.75 847.2048027 87.50457237 1.14623065 0.011462307

126 Feb-06 821.46 847.9560103 89.31537968 1.084643079 0.010846431

127 Mar-06 808.86 848.6826159 97.6164217 0.976349187 0.009763492

128 Apr-06 800.33 849.3854047 101.7102002 0.92640266 0.009264027

129 May-06 800.19 850.0651379 103.8383672 0.906531842 0.009065318

130 Jun-06 665.84 850.7225542 107.3118674 0.729346969 0.00729347

131 Jul-06 734.4 851.3583693 110.380944 0.781494911 0.007814949

132 Aug-06 830.84 851.9732773 109.7244943 0.888766827 0.008887668

133 Sep-06 878.63 852.567951 106.4237817 0.968363336 0.009683633

134 Oct-06 1036 853.1430426 104.0159813 1.167448768 0.011674488

135 Nov-06 931.12 853.699184 92.26314862 1.182149812 0.011821498

136 Dec-06 792.8 854.2369877 89.89484152 1.032405949 0.010324059


137 Jan-07 797.09 854.7570472 87.50457237 1.065697443 0.010656974

138 Feb-07 841.82 855.2599374 89.31537968 1.102033665 0.011020337

139 Mar-07 811.34 855.7462155 97.6164217 0.971258912 0.009712589

140 Apr-07 855.84 856.2164209 101.7102002 0.982753318 0.009827533

141 May-07 886.84 856.6710765 103.8383672 0.996949864 0.009969499

142 Jun-07 935.34 857.1106885 107.3118674 1.016915447 0.010169154

143 Jul-07 1142.48 857.5357472 110.380944 1.206986101 0.012069861

144 Aug-07 1231.13 857.9467274 109.7244943 1.307795999 0.01307796

145 Sep-07 1032.22 858.344089 106.4237817 1.129983656 0.011299837

146 Oct-07 974.51 858.728277 104.0159813 1.091014356 0.010910144

147 Nov-07 1045.7 859.0997226 92.26314862 1.319274772 0.013192748

148 Dec-07 925.87 859.4588431 89.89484152 1.198367871 0.011983679


149 Jan-08 1029.65 859.8060425 87.50457237 1.3685428 0.013685428

150 Feb-08 1049.03 860.1417119 89.31537968 1.36549983 0.013654998

151 Mar-08 1230.77 860.4662298 97.6164217 1.465278534 0.014652785

152 Apr-08 1233.72 860.7799627 101.7102002 1.409158832 0.014091588

153 May-08 1317.69 861.0832653 103.8383672 1.47370396 0.01473704

154 Jun-08 1414.43 861.3764807 107.3118674 1.530173574 0.015301736

155 Jul-08 1431.69 861.6599411 110.380944 1.505285868 0.015052859

156 Aug-08 1131.85 861.9339681 109.7244943 1.196771645 0.011967716

157 Sep-08 923.97 862.1988726 106.4237817 1.006958872 0.010069589

158 Oct-08 909.83 862.4549557 104.0159813 1.01420036 0.010142004

159 Nov-08 853.34 862.7025085 92.26314862 1.072093767 0.010720938

160 Dec-08 761.72 862.941813 89.89484152 0.981926712 0.009819267


161 Jan-09 782.89 863.1731418 87.50457237 1.036506621 0.010365066

162 Feb-09 766.46 863.3967585 89.31537968 0.99392321 0.009939232

163 Mar-09 847.05 863.6129185 97.6164217 1.004770863 0.010047709

164 Apr-09 904.52 863.8218685 101.7102002 1.029507395 0.010295074

165 May-09 888.24 864.0238474 103.8383672 0.990026334 0.009900263

166 Jun-09 816.12 864.2190862 107.3118674 0.879999479 0.008799995

167 Jul-09 715.36 864.4078084 110.380944 0.749742046 0.00749742

168 Aug-09 836.29 864.5902301 109.7244943 0.881541966 0.00881542

169 Sep-09 1030.95 864.7665604 106.4237817 1.120211504 0.011202115

170 Oct-09 1152.61 864.9370015 104.0159813 1.281143673 0.012811437

171 Nov-09 1154.41 865.101749 92.26314862 1.446320756 0.014463208

172 Dec-09 1013.58 865.260992 89.89484152 1.303095173 0.013030952


173 Jan-10 1089.26 865.4149135 87.50457237 1.438389267 0.014383893

174 Feb-10 981.59 865.5636904 89.31537968 1.269710897 0.012697109

175 Mar-10 954.72 865.7074938 97.6164217 1.129748985 0.01129749

176 Apr-10 994.73 865.8464893 101.7102002 1.129535296 0.011295353

177 May-10 1054.71 865.9808367 103.8383672 1.172916056 0.011729161

178 Jun-10 1201.27 866.1106909 107.3118674 1.292467049 0.01292467

179 Jul-10 1302.41 866.2362014 110.380944 1.362126018 0.01362126

180 Aug-10 1139.33 866.357513 109.7244943 1.198529696 0.011985297

181 Sep-10 1046.85 866.4747657 106.4237817 1.135245662 0.011352457

182 Oct-10 1086.32 866.5880945 104.0159813 1.205160771 0.012051608

183 Nov-10 823.35 866.6976305 92.26314862 1.029647594 0.010296476

184 Dec-10 723.89 866.8035001 89.89484152 0.929003071 0.009290031


185 Jan-11 734.61 866.9058255 87.50457237 0.968398633 0.009683986

186 Feb-11 884.96 867.004725 89.31537968 1.142814989 0.01142815

187 Mar-11 852.44 867.100313 97.6164217 1.007097676 0.010070977

188 Apr-11 880.97 867.1926999 101.7102002 0.998805665 0.009988057

189 May-11 836.41 867.2819927 103.8383672 0.928754726 0.009287547

190 Jun-11 916.4 867.3682947 107.3118674 0.984540952 0.00984541

191 Jul-11 971.56 867.4517057 110.380944 1.014682609 0.010146826

192 Aug-11 948.83 867.5323224 109.7244943 0.996779632 0.009967796

193 Sep-11 1194.94 867.6102381 106.4237817 1.294144419 0.012941444

194 Oct-11 1032.7 867.685543 104.0159813 1.144225823 0.011442258

195 Nov-11 681.65 867.7583245 92.26314862 0.851401437 0.008514014

196 Dec-11 757.73 867.8286669 89.89484152 0.971282847 0.009712828


197 Jan-12 730.58 867.8966517 87.50457237 0.961986593 0.009619866

198 Feb-12 778.64 867.9623578 89.31537968 1.00440663 0.010044066

199 Mar-12 802.57 868.0258614 97.6164217 0.947168778 0.009471688

200 Apr-12 822.89 868.0872361 101.7102002 0.931995692 0.009319957

201 May-12 755.83 868.1465533 103.8383672 0.838442395 0.008384424

202 Jun-12 952.76 868.2038817 107.3118674 1.02261943 0.010226194

203 Jul-12 1015.16 868.2592879 110.380944 1.059231665 0.010592317

204 Aug-12 970.39 868.3128362 109.7244943 1.018512828 0.010185128

205 Sep-12 1000.89 868.3645889 106.4237817 1.083042647 0.010830426

206 Oct-12 980.85 868.4146059 104.0159813 1.085863929 0.010858639

207 Nov-12 846.84 868.4629456 92.26314862 1.056870556 0.010568706

208 Dec-12 758.09 868.5096639 89.89484152 0.970982363 0.009709824


209 Jan-13 750.03 868.5548152 87.50457237 0.986848887 0.009868489

210 Feb-13 819.58 868.598452 89.31537968 1.056442957 0.01056443

211 Mar-13 908.1 868.6406251 97.6164217 1.0709536 0.010709536

212 Apr-13 980.49 868.6813833 101.7102002 1.109732091 0.011097321

213 May-13 1057.01 868.7207743 103.8383672 1.171766393 0.011717664

214 Jun-13 1157.65 868.7588436 107.3118674 1.241738897 0.012417389

215 Jul-13 1121.23 868.7956358 110.380944 1.169184299 0.011691843

216 Aug-13 1190.81 868.8311934 109.7244943 1.249118039 0.01249118

217 Sep-13 1119.72 868.865558 106.4237817 1.210927568 0.012109276

218 Oct-13 997.26 868.8987695 104.0159813 1.10341567 0.011034157

219 Nov-13 766 868.9308665 92.26314862 0.955466079 0.009554661

220 Dec-13 739.98 868.9618865 89.89484152 0.947293337 0.009472933


221 Jan-14 753.15 868.9918654 87.50457237 0.990455625 0.009904556

222 Feb-14 770.93 869.0208383 89.31537968 0.993249847 0.009932498

223 Mar-14 808.11 869.0488388 97.6164217 0.952584287 0.009525843

224 Apr-14 846.89 869.0758996 101.7102002 0.95808665 0.009580867

225 May-14 834.98 869.1020521 103.8383672 0.925225187 0.009252252

226 Jun-14 834.56 869.1273269 107.3118674 0.894800891 0.008948009

227 Jul-14 783.04 869.1517533 110.380944 0.81619557 0.008161956

228 Aug-14 768.17 869.1753598 109.7244943 0.805464396 0.008054644

229 Sep-14 771.03 869.1981739 106.4237817 0.833515699 0.008335157

230 Oct-14 732.15 869.2202222 104.0159813 0.809785833 0.008097858

231 Nov-14 717.87 869.2415304 92.26314862 0.895111352 0.008951114

232 Dec-14 769.23 869.2621233 89.89484152 0.984397917 0.009843979


233 Jan-15 758.02 869.2820249 87.50457237 0.99652734 0.009965273

234 Feb-15 704.17 869.3012584 89.31537968 0.906945023 0.00906945

235 Mar-15 633.29 869.3198462 97.6164217 0.746277163 0.007462772

236 Apr-15 612.13 869.3378099 101.7102002 0.69229403 0.00692294

237 May-15 608.64 869.3551706 103.8383672 0.674225849 0.006742258

238 Jun-15 629.9 869.3719484 107.3118674 0.675177923 0.006751779

239 Jul-15 640.11 869.3881629 110.380944 0.667032178 0.006670322

240 Aug-15 684.28 869.403833 109.7244943 0.717313011 0.00717313

241 Sep-15 631.91 869.4189769 106.4237817 0.682947667 0.006829477

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 2390

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Series1

Random Variation

t yt ∆yt ∆2yt ∆3yt ∆4yt ∆5yt ∆6yt ∆7yt ∆8yt ∆9yt ∆10yt ∆11yt

Sep-95 537.55 8.66

Oct-95 546.21 18.03 9.37 -148.41

Nov-95 564.24 -121.01 -139.04 234.35 382.76 -669.78

Dec-95 443.23 -25.7 95.31 -52.67 -287.02 320.03 989.81-

1331.69


Jan-96 417.53 16.94 42.64 -19.66 33.01 -21.85 -341.88 283.49 1615.18 -1502.62

Feb-96 434.47 39.92 22.98 -8.5 11.16 -80.24 -58.39 396.05 112.56 -1521.01 -18.39 5501.47

Mar-96 474.39 54.4 14.48 -77.58 -69.08 257.42 337.66 -1012.4 -1408.45 3962.07 5483.08 -15207.8

Apr-96 528.79 -8.7 -63.1 110.76 188.34 -417.32 -674.74 1541.22 2553.62 -5762.65 -9724.72 21622.47

May-96 520.09 38.96 47.66 -118.22 -228.98 449.16 866.48 -1667.81 -3209.03 6135.1 11897.75 -22582.5

Jun-96 559.05 -31.6 -70.56 101.96 220.18 -352.17 -801.33 1258.26 2926.07 -4549.63 -10684.7 16555.73

Jul-96 527.45 -0.2 31.4 -30.03 -131.99 104.76 456.93 -365.3 -1623.56 1321.37 5871 -4884.41

Aug-96 527.25 1.17 1.37 -57.26 -27.23 196.39 91.63 -667.49 -302.19 2307.96 986.59 -8071.26

Sep-96 528.42 -54.72 -55.89 111.9 169.16 -379.47 -575.86 1338.28 2005.77 -4776.71 -7084.67 17216.93

Oct-96 473.7 1.29 56.01 -98.41 -210.31 382.95 762.42 -1432.66 -2770.94 5355.55 10132.26 -20031.7

Nov-96 474.99 -41.11 -42.4 74.23 172.64 -287.29 -670.24 1151.95 2584.61 -4543.89 -9899.44 17698.97

Dec-96 433.88 -9.28 31.83 -40.42 -114.65 194.42 481.71 -807.33 -1959.28 3255.64 7799.53 -13022.4


Jan-97 424.6 -17.87 -8.59 39.35 79.77 -131.2 -325.62 489.03 1296.36 -1967.21 -5222.85 8244.96

Feb-97 406.73 12.89 30.76 -12.08 -51.43 32.21 163.41 -181.82 -670.85 1054.9 3022.11 -5518.29

Mar-97 419.62 31.57 18.68 -31.3 -19.22 13.8 -18.41 202.23 384.05 -1441.28 -2496.18 7341.02

Apr-97 451.19 18.95 -12.62 -36.72 -5.42 197.62 183.82 -855 -1057.23 3403.56 4844.84 -13206.3

May-97 470.14 -30.39 -49.34 155.48 192.2 -473.56 -671.18 1491.33 2346.33 -4957.87 -8361.43 17146.16

Jun-97 439.75 75.75 106.14 -125.88 -281.36 346.59 820.15 -1120.21 -2611.54 3826.86 8784.73 -13475.2

Jul-97 515.5 56.01 -19.74 -60.65 65.23 46.53 -300.06 95.11 1215.32 -863.57 -4690.43 4406.16

Aug-97 571.51 -24.38 -80.39 51.11 111.76 -158.42 -204.95 446.86 351.75 -1147.84 -284.27 2594.95

Sep-97 547.13 -53.66 -29.28 4.45 -46.66 83.49 241.91 -349.23 -796.09 1162.84 2310.68 -3551.17

Oct-97 493.47 -78.49 -24.83 41.28 36.83 -23.83 -107.32 17.52 366.75 -77.65 -1240.49 484.86

Nov-97 414.98 -62.04 16.45 54.28 13 -113.63 -89.8 306.62 289.1 -833.28 -755.63 2130.35

Dec-97 352.94 8.69 70.73 -46.35 -100.63 103.19 216.82 -237.56 -544.18 541.44 1374.72 -1053.08


Jan-98 361.63 33.07 24.38 -43.79 2.56 82.45 -20.74 -240.3 -2.74 863.08 321.64 -3253.23

Feb-98 394.7 13.66 -19.41 41.22 85.01 -178.59 -261.04 620.04 860.34 -2068.51 -2931.59 6765.59

Mar-98 408.36 35.47 21.81 -52.36 -93.58 180.41 359 -588.13 -1208.17 1765.49 3834 -4939.02

Apr-98 443.83 4.92 -30.55 34.47 86.83 -48.72 -229.13 -30.81 557.32 660.47 -1105.02 -4090.04

May-98 448.75 8.84 3.92 72.58 38.11 -308.66 -259.94 1186.98 1217.79 -4534.59 -5195.06 17406.35

Jun-98 457.59 85.34 76.5 -197.97 -270.55 618.38 927.04 -2129.82 -3316.8 7676.7 12211.29 -28375

Jul-98 542.93 -36.13 -121.47 149.86 347.83 -584.4 -1202.78 2230.08 4359.9 -8486.99 -16163.7 32409.97

Aug-98 506.8 -7.74 28.39 -86.71 -236.57 442.9 1027.3 -1897.01 -4127.09 7759.29 16246.28 -31137.3

Sep-98 499.06 -66.06 -58.32 119.62 206.33 -426.81 -869.71 1735.19 3632.2 -7131.68 -14891 29107.86

Oct-98 433 -4.76 61.3 -100.86 -220.48 438.67 865.48 -1764.29 -3499.48 7085.21 14216.89 -28488.1

Nov-98 428.24 -44.32 -39.56 117.33 218.19 -460.14 -898.81 1821.44 3585.73 -7185.99 -14271.2 28354.34

Dec-98 383.92 33.45 77.77 -124.62 -241.95 462.49 922.63 -1778.82 -3600.26 6897.15 14083.14 -26784.6


Jan-99 417.37 -13.4 -46.85 95.92 220.54 -393.7 -856.19 1518.07 3296.89 -5804.35 -12701.5 22192.94

Feb-99 403.97 35.67 49.07 -77.24 -173.16 268.18 661.88 -989.39 -2507.46 3687.09 9491.44 -13825.6

Mar-99 439.64 7.5 -28.17 17.78 95.02 -59.33 -327.51 190.24 1179.63 -647.03 -4334.12 2293.63

Apr-99 447.14 -2.89 -10.39 53.47 35.69 -196.6 -137.27 722.84 532.6 -2687.52 -2040.49 10076.65

May-99 444.25 40.19 43.08 -107.44 -160.91 388.97 585.57 -1432.08 -2154.92 5348.64 8036.16 -20350.7

Jun-99 484.44 -24.17 -64.36 120.62 228.06 -457.54 -846.51 1761.64 3193.72 -6965.85 -12314.5 27896.24

Jul-99 460.27 32.09 56.26 -108.86 -229.48 457.59 915.13 -2010.49 -3772.13 8615.9 15581.75 -35968.5

Aug-99 492.36 -20.51 -52.6 119.25 228.11 -637.77 -1095.36 2833.28 4843.77 -11770.9 -20386.8 47474.46

Sep-99 471.85 46.14 66.65 -290.41 -409.66 1100.15 1737.92 -4093.83 -6927.11 15316.8 27087.68 -57750.8

Oct-99 517.99 -177.62 -223.76 400.08 690.49 -1255.76 -2355.91 4295.86 8389.69 -15346.3 -30663.1 56327.64

Nov-99 340.37 -1.3 176.32 -165.19 -565.27 684.19 1939.95 -2660.75 -6956.61 10318.24 25664.54 -40083.9

Dec-99 339.07 9.83 11.13 -46.27 118.92 -36.61 -720.8 700.88 3361.63 -4101.16 -14419.4 19495.95


Jan-00 348.9 -25.31 -35.14 36.04 82.31 -56.53 -19.92 -38.65 -739.53 975.39 5076.55 -6470.25

Feb-00 323.59 -24.41 0.9 61.82 25.78 -115.1 -58.57 197.21 235.86 -418.31 -1393.7 1575.75

Mar-00 299.18 38.31 62.72 -27.5 -89.32 23.54 138.64 14.76 -182.45 -236.26 182.05 1074.65

Apr-00 337.49 73.53 35.22 -93.28 -65.78 176.94 153.4 -403.95 -418.71 1020.44 1256.7 -2714.38

May-00 411.02 15.47 -58.06 17.88 111.16 -73.61 -250.55 197.78 601.73 -437.24 -1457.68 646.86

Jun-00 426.49 -24.71 -40.18 55.43 37.55 -126.38 -52.77 362.27 164.49 -1248.06 -810.82 4703.32

Jul-00 401.78 -9.46 15.25 -33.4 -88.83 183.12 309.5 -721.3 -1083.57 2644.44 3892.5 -9485.48

Aug-00 392.32 -27.61 -18.15 60.89 94.29 -228.68 -411.8 839.57 1560.87 -2948.54 -5592.98 10163.97

Sep-00 364.71 15.13 42.74 -73.5 -134.39 199.09 427.77 -548.1 -1387.67 1622.45 4570.99 -4967.09

Oct-00 379.84 -15.63 -30.76 -8.8 64.7 78.76 -120.33 -313.32 234.78 1226.35 -396.1 -4893.66

Nov-00 364.21 -55.19 -39.56 134.66 143.46 -354.89 -433.65 1147.81 1461.13 -4063.41 -5289.76 15029.04

Dec-00 309.02 39.91 95.1 -76.77 -211.43 359.27 714.16 -1454.47 -2602.28 5675.87 9739.28 -21889.6


Jan-01 348.93 58.24 18.33 71.07 147.84 -381.04 -740.31 1619.12 3073.59 -6474.41 -12150.3 25338.44

Feb-01 407.17 147.64 89.4 -162.13 -233.2 497.77 878.81 -1781.7 -3400.82 6713.75 13188.16 -26071.8

Mar-01 554.81 74.91 -72.73 102.44 264.57 -405.12 -902.89 1531.23 3312.93 -6169.85 -12883.6 25427.96

Apr-01 629.72 104.62 29.71 -38.11 -140.55 223.22 628.34 -1325.69 -2856.92 6374.51 12544.36 -27972.5

May-01 734.34 96.22 -8.4 44.56 82.67 -474.13 -697.35 2191.9 3517.59 -9053.67 -15428.2 36302.54

Jun-01 830.56 132.38 36.16 -346.9 -391.46 1020.42 1494.55 -3344.18 -5536.08 11820.69 20874.36 -43755.9

Jul-01 962.94 -178.36 -310.74 282.06 628.96 -829.21 -1849.63 2940.43 6284.61 -11060.8 -22881.5 42624.36

Aug-01 784.58 -207.04 -28.68 81.81 -200.25 261.59 1090.8 -1835.77 -4776.2 8682.05 19742.86 -37193.4

Sep-01 577.54 -153.91 53.13 143.15 61.34 -483.38 -744.97 2070.08 3905.85 -8768.49 -17450.5 36370.5

Oct-01 423.63 42.37 196.28 -278.89 -422.04 841.73 1325.11 -2792.56 -4862.64 10151.47 18919.96 -38889

Nov-01 466 -40.24 -82.61 140.8 419.69 -625.72 -1467.45 2496.27 5288.83 -9817.61 -19969.1 38841.86

Dec-01 425.76 17.95 58.19 -65.23 -206.03 403.1 1028.82 -2032.51 -4528.78 9055.17 18872.78 -38152.4


Jan-02 443.71 10.91 -7.04 131.84 197.07 -600.59 -1003.69 2493.88 4526.39 -10224.5 -19279.6 41481.34

Feb-02 454.62 135.71 124.8 -271.68 -403.52 889.6 1490.19 -3204.18 -5698.06 11977.27 22201.72 -45755.6

Mar-02 590.33 -11.17 -146.88 214.4 486.08 -824.39 -1713.99 3075.03 6279.21 -11576.6 -23553.9 44053.34

Apr-02 579.16 56.35 67.52 -123.91 -338.31 536.65 1361.04 -2222.37 -5297.4 8922.85 20499.46 -35345.6

May-02 635.51 -0.04 -56.39 74.43 198.34 -324.68 -861.33 1403.08 3625.45 -5923.33 -14846.2 24379.3

Jun-02 635.47 18 18.04 -51.91 -126.34 217.07 541.75 -894.8 -2297.88 3609.79 9533.12 -14410.8

Jul-02 653.47 -15.87 -33.87 38.82 90.73 -135.98 -353.05 417.11 1311.91 -1267.87 -4877.66 4196.17

Aug-02 637.6 -10.92 4.95 -6.43 -45.25 -71.92 64.06 461.15 44.04 -1949.36 -681.49 7078.7

Sep-02 626.68 -12.4 -1.48 -123.6 -117.17 453.29 525.21 -1444.17 -1905.32 4447.85 6397.21 -13297.8

Oct-02 614.28 -137.48 -125.08 212.52 336.12 -465.67 -918.96 1098.36 2542.53 -2452.74 -6900.59 4397.06

Nov-02 476.8 -50.04 87.44 82.97 -129.55 -286.27 179.4 1188.15 89.79 -4956.27 -2503.53 20319.78

Dec-02 426.76 120.37 170.41 -332.85 -415.82 1081.28 1367.55 -3678.33 -4866.48 12859.98 17816.25 -45823.2


Jan-03 547.13 -42.07 -162.44 332.61 665.46 -1229.5 -2310.78 4315.17 7993.5 -15146.9 -28006.9 53701.63

Feb-03 505.06 128.1 170.17 -231.43 -564.04 774.89 2004.39 -2838.27 -7153.44 10547.77 25694.71 -39322.1

Mar-03 633.16 66.84 -61.26 -20.58 210.85 -58.99 -833.88 556.06 3394.33 -3079.57 -13627.3 14516.23

Apr-03 700 -15 -81.84 131.28 151.86 -336.81 -277.82 870.82 314.76 -2190.68 888.89 5019.72

May-03 685 34.44 49.44 -53.67 -184.95 256.19 593 -1005.1 -1875.92 3717.93 5908.61 -13592.2

Jun-03 719.44 30.21 -4.23 17.57 71.24 -155.91 -412.1 836.91 1842.01 -3965.69 -7683.62 17540.78

Jul-03 749.65 43.55 13.34 -67.1 -84.67 268.9 424.81 -1286.77 -2123.68 5891.47 9857.16 -25468.9

Aug-03 793.2 -10.21 -53.76 117.13 184.23 -593.06 -861.96 2481.02 3767.79 -9720.3 -15611.8 37292.09

Sep-03 782.99 53.16 63.37 -291.7 -408.83 1026 1619.06 -3471.49 -5952.51 11960.02 21680.32 -42123.2

Oct-03 836.15 -175.17 -228.33 325.47 617.17 -826.43 -1852.43 2536.02 6007.51 -8482.86 -20442.9 29561.63

Nov-03 660.98 -78.03 97.14 116.21 -209.26 -142.84 683.59 60.67 -2475.35 635.89 9118.75 -4045.5

Dec-03 582.95 135.32 213.35 -235.89 -352.1 601.42 744.26 -1778.79 -1839.46 5709.14 5073.25 -19186.5


Jan-04 718.27 112.78 -22.54 13.43 249.32 -433.11 -1034.53 2090.89 3869.68 -8404.13 -14113.3 32017.49

Feb-04 831.05 103.67 -9.11 -170.36 -183.79 623.25 1056.36 -2443.56 -4534.45 9500.09 17904.22 -36592.6

Mar-04 934.72 -75.8 -179.47 269.1 439.46 -763.95 -1387.2 2522.08 4965.64 -9188.26 -18688.4 35021.94

Apr-04 858.92 13.83 89.63 -55.39 -324.49 370.93 1134.88 -1700.54 -4222.62 7145.33 16333.59 -29181.9

May-04 872.75 48.07 34.24 -8.95 46.44 -194.73 -565.66 1222.17 2922.71 -5703.02 -12848.4 24047.82

Jun-04 920.82 73.36 25.29 -157.24 -148.29 461.78 656.51 -1558.14 -2780.31 5496.45 11199.47 -19650.8

Jul-04 994.18 -58.59 -131.95 156.25 313.49 -439.85 -901.63 1158 2716.14 -2954.83 -8451.28 7279.39

Aug-04 935.59 -34.29 24.3 29.89 -126.36 -183.48 256.37 919.31 -238.69 -4126.72 -1171.89 17613.12

Sep-04 901.3 19.9 54.19 -279.95 -309.84 992.2 1175.68 -3446.1 -4365.41 12314.51 16441.23 -44802.1

Oct-04 921.2 -205.86 -225.76 402.41 682.36 -1278.22 -2270.42 4503 7949.1 -16046.4 -28360.9 57235.25

Nov-04 715.34 -29.21 176.65 -193.45 -595.86 954.36 2232.58 -3594.28 -8097.28 12827.98 28874.36 -45309.3

Dec-04 686.13 -46.01 -16.8 165.05 358.5 -407.34 -1361.7 1136.42 4730.7 -3606.92 -16434.9 12407.69


Jan-05 640.12 102.24 148.25 116.21 -48.84 -632.62 -225.28 2260.2 1123.78 -7634.13 -4027.21 25535.28

Feb-05 742.36 366.7 264.46 -565.25 -681.46 1402.3 2034.92 -4250.15 -6510.35 13873.94 21508.07 -46672.7

Mar-05 1109.06 65.91 -300.79 155.59 720.84 -812.93 -2215.23 3113.44 7363.59 -11290.7 -25164.6 40347.1

Apr-05 1174.97 -79.29 -145.2 63.5 -92.09 85.28 898.21 -813.65 -3927.09 3891.8 15182.48 -16096.3

May-05 1095.68 -160.99 -81.7 56.69 -6.81 169.84 84.56 -848.94 -35.29 2978.01 -913.79 -9636.09

Jun-05 934.69 -186 -25.01 219.72 163.03 -594.54 -764.38 2093.78 2942.72 -7571.87 -10549.9 27114.53

Jul-05 748.69 8.71 194.71 -211.79 -431.51 734.86 1329.4 -2535.37 -4629.15 8992.78 16564.65 -32288.5

Aug-05 757.4 -8.37 -17.08 91.56 303.35 -471.11 -1205.97 1828.26 4363.63 -6731.06 -15723.8 24642.36

Sep-05 749.03 66.11 74.48 -76.2 -167.76 151.18 622.29 -539.17 -2367.43 2187.46 8918.52 -8881.76

Oct-05 815.14 64.39 -1.72 -92.78 -16.58 234.3 83.12 -719.14 -179.97 2224.22 36.76 -6766.1

Nov-05 879.53 -30.11 -94.5 124.94 217.72 -401.72 -636.02 1325.11 2044.25 -4505.12 -6729.34 15508.93

Dec-05 849.42 0.33 30.44 -59.06 -184 287.37 689.09 -1135.76 -2460.87 4274.47 8779.59 -16011.4


Jan-06 849.75 -28.29 -28.62 44.31 103.37 -159.3 -446.67 677.84 1813.6 -2957.34 -7231.81 12823.02

Feb-06 821.46 -12.6 15.69 -11.62 -55.93 71.87 231.17 -465.9 -1143.74 2633.87 5591.21 -13147.5

Mar-06 808.86 -8.53 4.07 4.32 15.94 -162.86 -234.73 1024.23 1490.13 -4922.37 -7556.24 21539.89

Apr-06 800.33 -0.14 8.39 -142.6 -146.92 626.64 789.5 -2408.01 -3432.24 9061.28 13983.65 -33971.9

May-06 800.19 -134.35 -134.21 337.12 479.72 -991.87 -1618.51 3221.03 5629.04 -10927 -19988.3 37863.4

Jun-06 665.84 68.56 202.91 -175.03 -512.15 610.65 1602.52 -2076.91 -5297.94 6948.16 17875.14 -23250.2

Jul-06 734.4 96.44 27.88 -76.53 98.5 136.26 -474.39 -426.69 1650.22 1573.07 -5375.09 -5897.49

Aug-06 830.84 47.79 -48.65 158.23 234.76 -764.82 -901.08 2796.6 3223.29 -9699.51 -11272.6 33339.97

Sep-06 878.63 157.37 109.58 -371.83 -530.06 1130.7 1895.52 -3679.62 -6476.22 12367.88 22067.39 -42476.7

Oct-06 1036 -104.88 -262.25 228.81 600.64 -653.4 -1784.1 2212.04 5891.66 -8041.44 -20409.3 30062.66

Nov-06 931.12 -138.32 -33.44 176.05 -52.76 -225.46 427.94 62.26 -2149.78 1611.9 9653.34 -11050.2

Dec-06 792.8 4.29 142.61 -102.17 -278.22 264.74 490.2 -475.62 -537.88 215.09 -1396.81 3949.41


Jan-07 797.09 44.73 40.44 -115.65 -13.48 279.32 14.58 -798.41 -322.79 2767.69 2552.6 -10641.8

Feb-07 841.82 -30.48 -75.21 150.19 265.84 -504.51 -783.83 1646.49 2444.9 -5321.54 -8089.23 17365.98

Mar-07 811.34 44.5 74.98 -88.48 -238.67 358.15 862.66 -1230.15 -2876.64 3955.21 9276.75 -12585.1

Apr-07 855.84 31 -13.5 31 119.48 -9.34 -367.49 -151.58 1078.57 646.82 -3308.39 -1728.93

May-07 886.84 48.5 17.5 141.14 110.14 -528.41 -519.07 1573.81 1725.39 -4390.5 -5037.32 11692.13

Jun-07 935.34 207.14 158.64 -277.13 -418.27 526.33 1054.74 -1091.3 -2665.11 2264.31 6654.81 -4325.23

Jul-07 1142.48 88.65 -118.49 -169.07 108.06 489.77 -36.56 -1492.1 -400.8 4593.89 2329.58 -14081.2

Aug-07 1231.13 -198.91 -287.56 428.76 597.83 -1038.89 -1528.66 2700.99 4193.09 -7157.68 -11751.6 18729.35

Sep-07 1032.22 -57.71 141.2 -12.3 -441.06 133.44 1172.33 -263.6 -2964.59 -179.9 6977.78 4988.66

Oct-07 974.51 71.19 128.9 -319.92 -307.62 1042.17 908.73 -3408.09 -3144.49 11786.54 11966.44 -42783.7

Nov-07 1045.7 -119.83 -191.02 414.63 734.55 -1457.19 -2499.36 5233.96 8642.05 -19030.7 -30817.2 70142.92

Dec-07 925.87 103.78 223.61 -308.01 -722.64 1277.41 2734.6 -5154.69 -10388.7 20294.98 39325.68 -78728.1


Jan-09 782.89 -16.43 -37.6 134.62 285.01 -539.77 -1123.09 1987.13 4132.55 -7308.96 -14945.7 26887.27

Feb-09 766.46 80.59 97.02 -120.14 -254.76 324.27 864.04 -1189.28 -3176.41 4632.65 11941.61 -17966.1

Mar-09 847.05 57.47 -23.12 -50.63 69.51 -0.97 -325.24 266.96 1456.24 -1391.83 -6024.48 5912.18

Apr-09 904.52 -16.28 -73.75 17.91 68.54 -59.25 -58.28 331.37 64.41 -1504.13 -112.3 6020.7

May-09 888.24 -72.12 -55.84 27.2 9.29 213.84 273.09 -1108.35 -1439.72 4404.27 5908.4 -16455.2

Jun-09 816.12 -100.76 -28.64 250.33 223.13 -621.42 -835.26 1856.2 2964.55 -6142.57 -10546.8 21315.71

Jul-09 715.36 120.93 221.69 -147.96 -398.29 399.52 1020.94 -1321.82 -3178.02 4626.3 10768.87 -16361.9

Aug-09 836.29 194.66 73.73 -146.73 1.23 98.64 -300.88 126.46 1448.28 -966.72 -5593.02 3537.83

Sep-09 1030.95 121.66 -73 -46.86 99.87 -75.78 -174.42 608.02 481.56 -3021.91 -2055.19 13612.43

Oct-09 1152.61 1.8 -119.86 -22.77 24.09 357.82 433.6 -1932.33 -2540.35 8535.33 11557.24 -35079.2

Nov-09 1154.41 -140.83 -142.63 359.14 381.91 -1140.91 -1498.73 4062.65 5994.98 -14986.6 -23522 55981.53

Dec-09 1013.58 75.68 216.51 -399.86 -759 1423.01 2563.92 -4929.01 -8991.66 17472.92 32459.56 -63251.7


Jan-10 1089.26 -107.67 -183.35 264.15 664.01 -942.08 -2365.09 3552.25 8481.26 -13319.2 -30792.2 49875.04

Feb-10 981.59 -26.87 80.8 -13.92 -278.07 245.08 1187.16 -1285.73 -4837.98 5763.64 19082.88 -24529.5

Mar-10 954.72 40.01 66.88 -46.91 -32.99 146.51 -98.57 -360.07 925.66 316.99 -5446.65 3109.1

Apr-10 994.73 59.98 19.97 66.61 113.52 -312.13 -458.64 882.58 1242.65 -2020.56 -2337.55 3035.23

May-10 1054.71 146.56 86.58 -132 -198.61 111.81 423.94 104.67 -777.91 -1322.88 697.68 6794.44

Jun-10 1201.27 101.14 -45.42 -218.8 -86.8 640.42 528.61 -1996.12 -2100.79 6169.24 7492.12 -18788.6

Jul-10 1302.41 -163.08 -264.22 334.82 553.62 -827.09 -1467.51 2072.33 4068.45 -5127.25 -11296.5 12034.96

Aug-10 1139.33 -92.48 70.6 61.35 -273.47 -222.27 604.82 1013.53 -1058.8 -4388.78 738.47 18369.32

Sep-10 1046.85 39.47 131.95 -434.39 -495.74 1396.08 1618.35 -4434.05 -5447.58 14719.01 19107.79 -50994.1

Oct-10 1086.32 -262.97 -302.44 465.95 900.34 -1419.62 -2815.7 4837.38 9271.43 -17167.3 -31886.3 62397.78

Nov-10 823.35 -99.46 163.51 -53.33 -519.28 602.06 2021.68 -3058.47 -7895.85 13344.21 30511.49 -54909.9

Dec-10 723.89 10.72 110.18 29.45 82.78 -434.73 -1036.79 2389.89 5448.36 -11054.2 -24398.4 47791.57


Jan-08 1029.65 19.38 -84.4 246.76 554.77 -1142.68 -2420.09 4751.64 9906.33 -19107.4 -39402.4 75511.29

Feb-08 1049.03 181.74 162.36 -341.15 -587.91 1188.87 2331.55 -4449.44 -9201.08 17001.49 36108.9 -65920.3

Mar-08 1230.77 2.95 -178.79 259.81 600.96 -929.02 -2117.89 3350.97 7800.41 -12809.9 -29811.4 50628.11

Apr-08 1233.72 83.97 81.02 -68.25 -328.06 304.06 1233.08 -1658.51 -5009.48 8006.84 20816.73 -35819.2

May-08 1317.69 96.74 12.77 -92.25 -24 -121.37 -425.43 1338.85 2997.36 -6995.64 -15002.5 31325.21

Jun-08 1414.43 17.26 -79.48 -237.62 -145.37 792.05 913.42 -2659.43 -3998.28 9327.09 16322.73 -33959.6

Jul-08 1431.69 -299.84 -317.1 409.06 646.68 -953.96 -1746.01 2669.38 5328.81 -8309.79 -17636.9 27943.69

Aug-08 1131.85 -207.88 91.96 101.78 -307.28 -30.59 923.37 -311.6 -2980.98 1997.02 10306.81 -9676.92

Sep-08 923.97 -14.14 193.74 -236.09 -337.87 581.18 611.77 -1295.56 -983.96 2626.91 629.89 -3888.41

Oct-08 909.83 -56.49 -42.35 7.22 243.31 -102.61 -683.79 347.39 1642.95 -631.61 -3258.52 -625.36

Nov-08 853.34 -91.62 -35.13 147.92 140.7 -439.01 -336.4 1358.73 1011.34 -4515.49 -3883.88 16036.07

Dec-08 761.72 21.17 112.79 -150.39 -298.31 583.32 1022.33 -2145.42 -3504.15 7636.7 12152.19 -27097.9


Jan-11 734.61 150.35 139.63 -322.5 -351.95 918.37 1353.1 -3215.95 -5605.84 12338.96 23393.16 -49025.4

Feb-11 884.96 -32.52 -182.87 243.92 566.42 -944.48 -1862.85 3517.17 6733.12 -13293.3 -25632.2 51039.33

Mar-11 852.44 28.53 61.05 -134.14 -378.06 709.84 1654.32 -3042.96 -6560.13 12113.87 25407.12 -46847.5

Apr-11 880.97 -44.56 -73.09 197.64 331.78 -678.8 -1388.64 2510.78 5553.74 -9326.53 -21440.4 34214.42

May-11 836.41 79.99 124.55 -149.38 -347.02 443.34 1122.14 -1262.01 -3772.79 3447.49 12774.02 -9237.36

Jun-11 916.4 55.16 -24.83 -53.06 96.32 303.47 -139.87 -1587.31 -325.3 6984.15 3536.66 -28016.5

Jul-11 971.56 -22.73 -77.89 346.73 399.79 -1423.71 -1727.18 5071.54 6658.85 -17495.7 -24479.9 59956.44

Aug-11 948.83 246.11 268.84 -677.19 -1023.92 1920.65 3344.36 -5765.34 -10836.9 17980.83 35476.56 -57539.8

Sep-11 1194.94 -162.24 -408.35 219.54 896.73 -500.33 -2420.98 1378.61 7143.95 -4082.39 -22063.2 12404.4

Oct-11 1032.7 -351.05 -188.81 615.94 396.4 -1542.7 -1042.37 4440.17 3061.56 -13741.2 -9658.82 44545.06

Nov-11 681.65 76.08 427.13 -530.36 -1146.3 1855.1 3397.8 -6239.48 -10679.7 21145.03 34886.24 -72728.6

Dec-11 757.73 -27.15 -103.23 178.44 708.8 -986.58 -2841.68 4225.9 10465.38 -16697.3 -37842.3 64162.9


Jan-12 730.58 48.06 75.21 -99.34 -277.78 397.64 1384.22 -2006.01 -6231.91 9623.29 26320.58 -43208.7

Feb-12 778.64 23.93 -24.13 20.52 119.86 -224.15 -621.79 1385.37 3391.38 -7264.79 -16888.1 34599.58

Mar-12 802.57 20.32 -3.61 -83.77 -104.29 539.43 763.58 -2488.04 -3873.41 10446.71 17711.5 -42624.1

Apr-12 822.89 -67.06 -87.38 351.37 435.14 -1185.03 -1724.46 4085.26 6573.3 -14465.9 -24912.6 52332.61

May-12 755.83 196.93 263.99 -398.52 -749.89 1175.77 2360.8 -3807.37 -7892.63 12954.04 27419.97 -45663

Jun-12 952.76 62.4 -134.53 27.36 425.88 -270.8 -1446.57 1254.04 5061.41 -5288.96 -18243 21688.71

Jul-12 1015.16 -44.77 -107.17 182.44 155.08 -463.33 -192.53 1026.49 -227.55 -1843.25 3445.71 1216.26

Aug-12 970.39 30.5 75.27 -125.81 -308.25 370.63 833.96 -1044.31 -2070.8 2818.72 4661.97 -6993.73

Sep-12 1000.89 -20.04 -50.54 -63.43 62.38 160.28 -210.35 -296.39 747.92 486.96 -2331.76 -862.66

Oct-12 980.85 -134.01 -113.97 159.23 222.66 -346.46 -506.74 938.49 1234.88 -2707.46 -3194.42 8107.04

Nov-12 846.84 -88.75 45.26 35.43 -123.8 85.29 431.75 -534.09 -1472.58 2205.16 4912.62 -8192.28

Dec-12 758.09 -8.06 80.69 -3.08 -38.51 -17.05 -102.34 198.49 732.58 -1074.5 -3279.66 4799.34


Jan-13 750.03 69.55 77.61 -58.64 -55.56 79.1 96.15 -143.43 -341.92 445.18 1519.68 -2065.77

Feb-13 819.58 88.52 18.97 -35.1 23.54 31.82 -47.28 -40.17 103.26 -100.91 -546.09 1574.05

Mar-13 908.1 72.39 -16.13 20.26 55.36 -55.63 -87.45 -37.82 2.35 927.05 1027.96 -6021.68

Apr-13 980.49 76.52 4.13 19.99 -0.27 -180.9 -125.27 891.58 929.4 -4066.67 -4993.72 17642.4

May-13 1057.01 100.64 24.12 -161.18 -181.17 585.41 766.31 -2245.69 -3137.27 8582.01 12648.68 -32902.6

Jun-13 1157.65 -36.42 -137.06 243.06 404.24 -893.97 -1479.38 3199.05 5444.74 -11671.9 -20253.9 43490.22

Jul-13 1121.23 69.58 106 -246.67 -489.73 825.7 1719.67 -3028.07 -6227.12 11564.49 23236.35 -44818.2

Aug-13 1190.81 -71.09 -140.67 89.3 335.97 -482.7 -1308.4 2309.3 5337.37 -10017.3 -21581.8 41482.65

Sep-13 1119.72 -122.46 -51.37 -57.43 -146.73 518.2 1000.9 -2370.66 -4679.96 9883.5 19900.83 -39977.5

Oct-13 997.26 -231.26 -108.8 314.04 371.47 -851.56 -1369.76 2832.88 5203.54 -10193.2 -20076.7 38110.14

Nov-13 766 -26.02 205.24 -166.05 -480.09 611.56 1463.12 -2156.78 -4989.66 7840.24 18033.44 -29338.1

Dec-13 739.98 13.17 39.19 -34.58 131.47 -82.1 -693.66 693.8 2850.58 -3464.46 -11304.7 15373.92


Jan-14 753.15 17.78 4.61 14.79 49.37 -81.96 0.14 79.92 -613.88 604.76 4069.22 -5274.72

Feb-14 770.93 37.18 19.4 -17.8 -32.59 -1.9 80.06 70.8 -9.12 -600.74 -1205.5 3857.71

Mar-14 808.11 38.78 1.6 -52.29 -34.49 148.96 150.86 -539.06 -609.86 2051.47 2652.21 -8094.31

Apr-14 846.89 -11.91 -50.69 62.18 114.47 -239.24 -388.2 902.55 1441.61 -3390.63 -5442.1 12683.47

May-14 834.98 -0.42 11.49 -62.59 -124.77 275.11 514.35 -1046.47 -1949.02 3850.74 7241.37 -14072

Jun-14 834.56 -51.52 -51.1 87.75 150.34 -257.01 -532.12 855.25 1901.72 -2979.86 -6830.6 10693.78

Jul-14 783.04 -14.87 36.65 -18.92 -106.67 66.12 323.13 -222.89 -1078.14 883.32 3863.18 -3809.34

Aug-14 768.17 2.86 17.73 -59.47 -40.55 166.36 100.24 -417.71 -194.82 937.16 53.84 -1603.79

Sep-14 771.03 -38.88 -41.74 66.34 125.81 -151.11 -317.47 324.63 742.34 -612.79 -1549.95 657.82

Oct-14 732.15 -14.28 24.6 41.04 -25.3 -143.95 7.16 454.18 129.55 -1504.92 -892.13 5331.38

Nov-14 717.87 51.36 65.64 -128.21 -169.25 317.39 461.34 -921.19 -1375.37 2934.33 4439.25 -9923.63

Dec-14 769.23 -11.21 -62.57 19.93 148.14 -142.46 -459.85 637.77 1558.96 -2550.05 -5484.38 9832.11


Jan-15 758.02 -53.85 -42.64 25.61 5.68 35.46 177.92 -353.32 -991.09 1797.68 4347.73 -7903.08

Feb-15 704.17 -70.88 -17.03 66.75 41.14 -139.94 -175.4 453.27 806.59 -1757.67 -3555.35 7187.55

Mar-15 633.29 -21.16 49.72 -32.05 -98.8 137.93 277.87 -497.81 -951.08 1874.53 3632.2 -7441.53

Apr-15 612.13 -3.49 17.67 7.08 39.13 -82.01 -219.94 425.64 923.45 -1934.8 -3809.33

May-15 608.64 21.26 24.75 -35.8 -42.88 123.69 205.7 -585.71 -1011.35

Jun-15 629.9 10.21 -11.05 45.01 80.81 -256.32 -380.01

Jul-15 640.11 44.17 33.96 -130.5 -175.51

Aug-15 684.28 -52.37 -96.54

Sep-15 631.91

SUM OF SQUARES 1925970.97

3053046.68

8037003.39

25111935.5

84201102.1 293558473

1050330682

3827992574

14143203466

52803972269 1.99E+11

H values 32.379 45.4724 56.8974 67.0484 76.1734 84.4292 91.9274 98.7588 105.9592 110.6842

µ'2(∆yt) 8024.879 V1 4012.44 R1 15.19836

µ'2(∆2yt) 12774.254 V2 2129.042 R2 9.410319

µ'2(∆3yt) 33768.922 V3 1688.446 R3 5.889315

µ'2(∆4yt) 105957.53 V4 1513.679 R4 4.335072

µ'2(∆5yt) 356784.33 V5 1415.811 R5 3.436817

µ'2(∆6yt) 1249185 V6 1351.932 R6 2.752007

µ'2(∆7yt) 4488592.7 V7 1307.865 R7 2.201323

µ'2(∆8yt) 16429153 V8 1276.546 R8 1.756052

µ'2(∆9yt) 60962084 V9 1253.848 R9 1.402978

µ'2(∆10yt) 228588625 V10 1237.246 R10 1.087325

µ'2(∆11yt) 864218897 V11 1225.092

Thank you

Time series analysis

Data & Analytics

Transcript of Time series analysis