IBS Statistics Year 1Dr. Ning DING

Table of content• Review

• Learning Goals

• Chapter 16: Time Series and Forecasting

• Exercises

Chapter 3: Describing Data

Review Chapter 3Why Dispersion?Why Dispersion?Central Tendency?Central Tendency?

Chapter 3: Describing Data

Review Chapter 3DispersionDispersion

Range Variation Standard Deviation

Chapter 3: Describing Data

Review Chapter 3DispersionDispersion

Chapter 4: Describing Data

P42 Example Ch2

The distribution is skewed to __________because the mean is __________the median.

the right larger than

Interquartile Range

Mean =23.06

Review Chapter 4

Review Chapter 4

Chapter 4: Describing Data

23456789

23456789

2345671013

2345671013

2344.254.75789

2344.254.75789

233.253.503.75459

233.253.503.75459

Mean= 5.5 6.25 5.25 4.19Mean= 5.5 6.25 5.25 4.19

Median= 5.5 5.5 4.5 3.38Median= 5.5 5.5 4.5 3.38

Review Chapter 4

Chapter 4: Describing Data

Mean= 5.5 6.25 5.25 4.19Mean= 5.5 6.25 5.25 4.19

Median= 5.5 5.5 4.5 3.38Median= 5.5 5.5 4.5 3.38Most skewed?Most skewed?

http://qudata.com/online/statcalc/

Chapter 12: Sim Reg & Corr

Sample Exam P.4

Ŷ = a + bXŶ = a + bX a = -1.8181

Review Chapter 12

Chapter 12: Sim Reg & Corr

Review Chapter 12

Negative CorrelationNegative CorrelationPositive CorrelationPositive Correlation

Chapter 12: Sim Reg & Corr

Exercise

Sample Exam P.4

xn-x

y xn-xy=b

22

Ŷ = -1.8182 + 0.1329XŶ = -1.8182 + 0.1329X

a = -1.8181

Applicable when time series follows fairly linear trend that have definite rhythmic pattern

Chapter 16: Time Series & Forecasting

Review Chapter 16

1+2+3+4+5+4+3=22 / 7 = 3.143

Seven-Year Moving Total Moving Average

2+3+4+5+4+3+2=23 / 7 = 3.2863+4+5+4+3+2+3=24 / 7 = 3.429

Learning Goals• Chapter 16:

– Define the components of a time series– Compute a moving average– Determine a linear trend equation– Compute a trend equation for a nonlinear trend– Use a trend equation to forecast future time periods and to

develop seasonally adjusted forecasts– Determine and interpret a set of seasonal indexes– Desearsonalize data using a seasonal index– Test for autocorrelation

ExerciseChapter 16: Time Series & Forecasting

Ŷ = a + btŶ = a + btxn-x

y xn-xy=b

22 a = Y - bX

16*7140

67.22*4*71.683

-

-=b = 1.73a = 22.67 -1.73*4 = 15.75

P152 N6 Ch16

3. Linear TrendChapter 16: Time Series & Forecasting

Ŷ = a + btŶ = a + btxn-x

y xn-xy=b

22 a = Y - bX

= 1.7328

3.48=b Ŷ = 22.67 + 1.73tŶ = 22.67 + 1.73ta = 22.67 = 22.67

x

xy=b

2

3. Linear TrendChapter 16: Time Series & Forecasting

Ŷ = a + btŶ = a + bt a = Y - bXx

xy=b

2

Odd-numbered

Odd-numbered

Even-numbered

Even-numbered

4. Seasonal Variation

Understanding seasonal fluctuations help plan for sufficient goods and materials on hand to meet varying seasonal demand

Chapter 16: Time Series & Forecasting

4. Seasonal VariationChapter 16: Time Series & Forecasting

Seasonal variations are fluctuations that coincide with certain seasons and are repeated year after year

4. Seasonal VariationChapter 16: Time Series & Forecasting

Seasonal Index:A number, usually expressed in percent, that expresses the relative value of a season with respect to the average for the year (100%)

Sales for December are 26.8% above an average month.

Sales for July are 14% below an average month.

4. Seasonal VariationChapter 16: Time Series & Forecasting

200520062007200820092010

Sales Report: in $ millionsSales Report: in $ millions

4. Seasonal VariationChapter 16: Time Series & Forecasting

200520062007200820092010

Step 1: Re-organize the dataStep 1: Re-organize the data

6.7+4.6+10.0+12.7=34 /4=8.504.6+10.0+12.7+6.5=33.8 /4=8.45

Step 2: Moving AverageStep 2: Moving Average

Step 3: Centered Moving AverageStep 3: Centered Moving Average

Step 4: Specific Seasonal IndexStep 4: Specific Seasonal Index

10/8.475=1.18012.7/8.45=1.5036.5/8.425=0.772

Step 4: Specific Seasonal IndexStep 4: Specific Seasonal Index

200520062007200820092010

+ + + =

Step 5: Typical Quarterly IndexStep 5: Typical Quarterly Index

*(0.9978)*(0.9978) *(0.9978)*(0.9978) *(0.9978)*(0.9978) *(0.9978)*(0.9978)

200520062007200820092010

Step 6: InterpretStep 6: Interpret

Sales for the Fall are 51.9% above the typical quarter. Sales for the Fall are 51.9% above the typical quarter.

Sales for the Winter are 23.5% below the typical quarter.Sales for the Winter are 23.5% below the typical quarter.

Appliance Center sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in $ millions) were reported.

Determine a typical seasonal index for each of the four quarters.

ExerciseChapter 16: Time Series & Forecasting

P161 No.10 Ch16

ExerciseChapter 16: Time Series & Forecasting

P161 No.10 Ch16

Step 1: Reorganize the data

Step 1: Reorganize the data

Step 2: Moving Average

Step 2: Moving Average

Step 3: Centered Moving Average

Step 3: Centered Moving Average

Step 4: Specific

Seasonal Index

Step 4: Specific

Seasonal Index

ExerciseChapter 16: Time Series & Forecasting

P161 No.10 Ch16

Step 5: Reorganize the data

Step 5: Reorganize the data

Step 6: Calculate the mean for each quarter

Step 6: Calculate the mean for each quarter

Step 7: Sum up

the four means

Step 7: Sum up

the four means

Step 8: Divide 4

by Total of four

means to get

Correction

Factor

Step 8: Divide 4

by Total of four

means to get

Correction

Factor

Step 9: Mean * C

orrection Factor

Step 9: Mean * C

orrection Factor

5. Deseasonalizing DataChapter 16: Time Series & Forecasting

To remove the seasonal fluctuations so that the trend and cycle can be studied.

Ŷ = a + bXŶ = a + bX Ŷ = a + btŶ = a + bt

5. Deseasonalizing DataChapter 16: Time Series & Forecasting

76.5 57.5 114.1 151.9

/ 0.765 = 8.759

/ 0.575 = 8.004

/ 1.141 = 8.761/ 1.519 = 8.361

/ 0.765/ 0.575

/ 1.141/ 1.519/ 0.765/ 0.575

/ 1.141/ 1.519

= 8.498= 8.004

= 8.586= 8.953= 9.021= 8.700

= 9.112= 9.283

Ŷ = a + btŶ = a + bt

Ŷ = 8.1096 + 0.0899 tŶ = 8.1096 + 0.0899 t

Sale increased at a rate of 0.0899 ($ millions) per quarter.Sale increased at a rate of 0.0899 ($ millions) per quarter.

Ŷ = 8.1096 + 0.0899 * 25= 10.3571 $ millionsŶ = 8.1096 + 0.0899 * 25= 10.3571 $ millions

10.3571*0.765 = 7.9232 $ millions10.3571*0.765 = 7.9232 $ millions

Chapter 16: Time Series & Forecasting

76.5 57.5 114.1 151.9

ExerciseChapter 16: Time Series & Forecasting

1. Calculate the seasonal indices for each quarter, express them as a ratio and not as a %. You may round to 4 dec. places.

2. Interpret the seasonal index quarter II.

3. Deseasonalized the original revenue for 2008 quarter I.

4. For 2011 quarter II the forecasted revenue from the trend line was 55. Calculate the seasonalized revenue for 2011 quarter II.

Friday Oct 22, 2010

Pigeon hole Ning Ding

Friday Oct 22, 2010

Pigeon hole Ning Ding

Summary• Chapter 16:

– A seasonal factor can be estimated using the ratio-to-moving-average method.

– The six-step procedure yields a seasonal index for each period.

– The seasonal factor is used to adjust forecasts, taking into account the effects of the season.

Chapter 16: Time Series & Forecasting

Step 1: Reorganize the data

Step 1: Reorganize the data

Step 2: Moving Average

Step 2: Moving Average

Step 3: Centered Moving Average

Step 3: Centered Moving Average

Step 4: Specific

Seasonal Index

Step 4: Specific

Seasonal Index

Step 5: Reorganize the data

Step 5: Reorganize the data

Step 6: Calculate the mean for each quarter

Step 6: Calculate the mean for each quarter

Step 7: Sum up

the four means

Step 7: Sum up

the four means

Step 8: Divide 4

by Total of four

means to get

Correction

Factor

Step 8: Divide 4

by Total of four

means to get

Correction

Factor

Step 9: Mean * C

orrection Factor

Step 9: Mean * C

orrection Factor

Hint