Demand Forecasting

Demand Forecasting

• Forecasting is the process of estimating future demand in terms of the quantity, timing, quality and location for desired products and services

Types of Forecasts

• Long Term (2-10 years)

• Intermediate Term (1-24 months)

• Short Term (1-5 weeks)

Long Term Forecast

• Time Horizon : 2 - 10 years

• Types of Products/services to offer

• Types & Sizes of Markets to serve

• Processes & Technologies to employ

• Plant location & size

Intermediate Term Forecast

• Time Horizon : 1 - 24 months

• Size of Work Force to employ

• Kinds & amounts of inventories to maintain

• Amount of desired subcontracting when needed

• Amount of desired overtime

Short Term Forecast

• Time Horizon : 1 - 5 week

• Assignment of orders to special facilities and personnel

• Dispatching to meet delivery times

The Forecasting System

• Forecasting Outputs

• Forecasting Inputs

• Constraints

• Decisions

• Performance Criteria

Forecasting System

Forecasting MethodsPredictiveCausalTime SeriesRoutine Short Term

Outputs

Estimates of Long,Medium & Short Term Demand

Forecast Error

Inputs

Internal Data:Historical, Subjective, Survey

Environmental Data: Social, Economic, Political, Technological

Performance Criteria

Accuracy, Stability, Responsiveness, Objective, Preparation Time

Constraints

Data, Time, Experience, Funds

Decisions

Selection of Data & Method

Forecasting : Outputs

• Forecast of Expected Demand and not future sales. Demand relates to orders received, sales refer to shipments made.

• Output expressed in appropriate form - marketing, production, finance.

• Translate demand for output units into requirements for various production inputs.

Forecasting System : Inputs• Data from Internal and/or external sources.

• Historical Data in the form of a time series; Expert opinions of an organization’s personnel; Results of special surveys

• External sources : industry experts, private consulting firms and government agencies.

• Internal for short/medium term, external for long term.

Forecasting System : Constraints

• Time available to prepare a forecast

• Lack of relevant data from internal & external sources.

• Quality of available data

• Expertise within the organization

• Available computing facilities

Forecasting System : Decisions• Decision with respect to data and method

• Data may be required in a particular form, or may require adjustment or aggregation.

• For a long history of demand, care has to be exercised for “how far back to go”

• Choice of method to prepare forecast will depend on data available, time needed and expertise that can be secured.

Forecasting System : Performance Criteria

• Accuracy of the forecast : Idle resources or shortages

• Time required to prepare a forecast

• Benefit to cost ratio

Forecasting Methods

• Predictive or Subjective (Estimates Survey & Delphi Method)

• Causal (Regression Analysis, Econometric Models & Input Output Models)

• Time Series (Trend, Seasonal, Cyclical, Random)

• Routine Short Term Forecasting (Moving Averages and Exponential Smoothing)

Routine Short Term Forecasting

• Short Term forecasts are related to specific product & services. It relies on historical data. The method should be programmed on a computer for frequent updates and forecasts for scheduling & inventory control

• Simple & Weighted Moving Averages• Exponential Smoothing• Measurement & Control of Forecast Errors

Simple & Weighted Moving Averages

• Next Period’s demand is a simple moving average. Equal or different weights to the periods can be given.

• Fluctuations are smoothened with more number of periods in the moving average (3, 5 or 7)

• Good when the demand is changing slowly.

• Can only forecast for one period ahead

Week Actual Forecast Absolute Forecast Absolute Forecast AbsoluteDemand N = 3 wk Deviation N = 5 wk Deviation N = 7 wk Deviation

1 100.02 125.03 90.04 110.05 105.06 130.07 85.08 102.0 106.7 4.7 104.0 2.0 106.4 4.49 110.0 105.7 4.3 106.4 3.6 106.7 3.310 90.0 99.0 9.0 106.4 16.4 104.6 14.611 105.0 100.7 4.3 103.4 1.6 104.6 0.412 95.0 101.7 6.7 98.4 3.4 103.9 8.913 115.0 96.7 18.3 100.4 14.6 102.4 12.614 120.0 105.0 15.0 103.0 17.0 100.3 19.715 80.0 110.0 30.0 105.0 25.0 105.3 25.316 95.0 105.0 10.0 103.0 8.0 102.1 7.117 100.0 98.3 1.7 101.0 1.0 100.0 0.0

Total AbsoluteDeviation 104.0 92.6 96.3Mean AbsoluteDeviation 10.4 9.3 9.6

Lowest

Moving Averages

Week Actual Forecast Absolute Forecast Absolute Forecast AbsoluteDemand N = 3 wk Deviation N = 3 wk Deviation N = 3 wk Deviation

1 100.02 125.03 90.04 110.0 105.0 5.0 102.5 7.5 105.5 4.55 105.0 108.3 3.3 107.0 2.0 111.5 6.56 130.0 101.7 28.3 103.5 26.5 99.0 31.07 85.0 115.0 30.0 118.5 33.5 112.5 27.58 102.0 106.7 4.7 102.5 0.5 108.5 6.59 110.0 105.7 4.3 102.5 7.5 110.9 0.910 90.0 99.0 9.0 102.6 12.6 95.1 5.111 105.0 100.7 4.3 98.4 6.6 102.0 3.012 95.0 101.7 6.7 101.5 6.5 103.0 8.013 115.0 96.7 18.3 97.0 18.0 95.5 19.514 120.0 105.0 15.0 107.0 13.0 104.0 16.015 80.0 110.0 30.0 113.5 33.5 106.0 26.016 95.0 105.0 10.0 99.0 4.0 109.5 14.517 100.0 98.3 1.7 95.5 4.5 103.0 3.0

Total AbsoluteDeviation 104.0 106.7 102.5Mean AbsoluteDeviation 6.9 7.1 6.8

Lowest

Weighted Moving AveragesEqual Weights Weights 0.2,0.3,0.5 Weights 0.5,0.3.0.2

Exponential Smoothing

• Exponential smoothing takes the forecast of the prior period and adds an adjustment to obtain the forecast of the current period

• The adjustment is a proportion of the forecast error (actual minus estimate)

• Forecastt= Forecastt-1 + α(Actualt-1 - Forecastt-1)

• α is a constant with value 0 to 1. Values of a are 0.1, 0.2, 0.3, or 0.5

Week Actual Forecast Absolute Forecast Absolute Forecast AbsoluteDemand a = 0.1 Deviation a = 0.2 Deviation a = 0.3 Deviation

1 100.02 125.03 90.04 110.05 105.06 130.07 85.0 85.0 85.0 85.08 102.0 85.0 17.0 85.0 17.0 85.0 17.09 110.0 86.7 23.3 88.4 21.6 90.1 19.910 90.0 89.0 1.0 92.7 2.7 96.1 6.111 105.0 89.1 15.9 92.2 12.8 94.2 10.812 95.0 90.7 4.3 94.7 0.3 97.5 2.513 115.0 91.1 23.9 94.8 20.2 96.7 18.314 120.0 93.5 26.5 98.8 21.2 102.2 17.815 80.0 96.2 16.2 103.1 23.1 107.5 27.516 95.0 94.6 0.4 98.5 3.5 99.3 4.317 100.0 94.6 5.4 97.8 2.2 98.0 2.0

Total AbsoluteDeviation 133.8 124.5 126.1Mean AbsoluteDeviation 13.4 12.5 12.6

Lowest

Exponential Smoothing

Causal Forecasting Methods

• Identify one or more variables which influence demand. Select the form of relationships. Validate the forecasting model to satisfy common sense and statistical tests

• Regression analysis models - Two variable, multiple variables

• Econometric Models

Regression Analysis Models

• Demand is dependent variable, causative factors are independent variables

• Coefficient of Determination indicates the proportion of variation in demand explained by independent variable.

Regression Method• Regression Method can be used for

Demand Forecasting.

• Historical Yearly Data can be used to forecast for future years.

• Make a Scatter Plot and calculate Correlation Coefficient.

• If Correlation Coefficient is +/- 0.7 or more, linear regression (Y = a + bX) can be used, where X is Year and Y is Demand.

Two Variable Regression – Least Square method

• Causal Relationship between Demand Y and Causative Factor X (X – Price, Income)

• Y = a + bX, Y= demand, X=causative factor• Method of Least Squares• ΣY = Na + bΣX …. (1) Σ - Sum• ΣXY = a ΣX + bΣX2 …. (2)• Values of a & b can be derived by solving

above 2 simultaneous equations• a = (ΣX2 ΣY –ΣXΣXY)/(nΣX2 – (ΣX)2)• b = (n ΣXY – ΣXΣY)/(n ΣX2 – (ΣX)2 )

Y = a + bX∑Y = Na + b ∑X Summing up ….Eq 1

Y = a + bXXY = aX + bX2 Multiplying by X∑XY = a∑X + b ∑X2 Summing Up … Eq 2

a = (∑Y - b ∑X )/N∑XY = (∑Y - b ∑X ) ∑X/N + b ∑X2

= ∑X ∑Y/N - b (∑X)2/N + b ∑X2

N∑XY = ∑X ∑Y - b (∑X)2 + N b ∑X2

N b ∑X2 - b (∑X)2 = N∑XY - ∑X ∑Y b = (N∑XY- ∑X ∑Y)/(N ∑X2 – (∑X)2)Similarly derive for aa = (ΣX2 ΣY –ΣXΣXY)/(NΣX2 – (ΣX)2)

Time Annual Time AnnualPeriod Sales Period Sales

Year X Y X2 XY Year X Y X2 XY1 1 1000 1 1000 1 -5 1000 25 -50002 2 1300 4 2600 2 -4 1300 16 -52003 3 1800 9 5400 3 -3 1800 9 -54004 4 2000 16 8000 4 -2 2000 4 -40005 5 2000 25 10000 5 -1 2000 1 -20006 6 2000 36 12000 6 1 2000 1 20007 7 2200 49 15400 7 2 2200 4 44008 8 2600 64 20800 8 3 2600 9 78009 9 2900 81 26100 9 4 2900 16 1160010 10 3200 100 32000 10 5 3200 25 16000

Total 55 21000 385 133300 0 21000 110 20200

11 11 3286.68 11 6 3201.8412 12 3502.44 12 7 3385.48

133300 = 55a + 385b

a = 913.32, b = 215.76

Y = 913.32 + 215.76X

Y = a + bXSum Y = Na + bSumX

Sum XY = aSumX + bSumX2

21000 = 10a + 55b

Y = a + bXSum Y = Na + bSumX

Sum XY = aSumX + bSumX2

Simple Linear Regression

20200 = 0 + 110b21000 = 10a + 0

a = 2100, b = 183.64

Y = 2100 + 183.64X

Coefficient of Determination

• Exam Score is dependent on Study Hours

• Study Hours (X) vs Exam Score (Y). More the study hours, higher is the exam score.

• Analyze Available Data. Calculate Coefficient of Determination (r2)and Correlation Coefficient (r)

• Coefficient of Determination gives the % of explained Variations

StudentStudy Hours

Exam Score Y' = a + bX SSE SSR SST

SrNo X Y Y' = 49.477+1.964X (Y-Y' )2 (Y'-AVG(Y) )2(Y - Avg(Y))2

1 21 Tom 1 53 51.44 2.43 348.15 292.412 Mary 5 74 59.30 216.16 116.69 15.213 Sarah 7 59 63.23 17.86 47.26 123.214 Oscar 8 43 65.19 492.39 24.11 734.415 Cullyn 10 56 69.12 172.08 0.96 198.816 Jaime 11 84 71.08 166.87 0.96 193.217 Theresa 14 96 76.97 361.98 47.26 670.818 Knut 15 69 78.94 98.77 78.12 1.219 Jim 15 84 78.94 25.62 78.12 193.21

10 Courtney 19 83 86.79 14.40 278.71 166.41

Sum 105 701 701 1568.56 1020.34 2588.90Average 10.5 70.1Observns 10

Coefficient of Determination = 1- (1568.56/2588.90) 0.3941

Variations Explained

= (Corelation Coeff)2 = (0.62779)2 0.3941 39.41%

Standard Error = √ 1568.56/(10-2) 14.0025

Study Hours VS Exam Score

y = 1.9641x + 49.477

R2 = 0.3941

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18 20

Study Hours

Exam

Sco

re Series1

Linear (Series1)

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.627790986R Square 0.394121523Adjusted R Square 0.318386713Standard Error 14.00249438Observations 10

ANOVAdf SS MS F Significance F

Regression 1 1020.34121 1020.34121 5.203967954 0.051972204Residual 8 1568.55879 196.0698488Total 9 2588.9

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept 49.47712665 10.06646125 4.915046652 0.001171307 26.26382541 72.6904279 26.26382541 72.6904279X Variable 1 1.964083176 0.86097902 2.281220716 0.051972204 -0.021338002 3.949504354 -0.021338002 3.949504354

Orders OrdersShip

Costs SSE SSR SST

SrNo X Y Avg(X) Avg(Y) X -Avg(x) Y - Avg(Y) (X -Avg(x))(Y-AVG(Y)) (X -Avg(X))2 (Y -Avg(Y))2 Y' = a + bX (Y-Y' )2 (Y'-AVG(Y) )2 (Y - Avg(Y))2

1 2 3 4 5 6 5 x 61 1 1068 4489 958.92 4698.3 109.0833 -209.3333333 -22834.77778 11899.1736 43820.4444 5236.35 558530.42 289460.78 43820.442 2 1026 5611 958.92 4698.3 67.08333 912.6666667 61224.72222 4500.17361 832960.444 5029.20 338492.94 109471.78 832960.443 3 767 3290 958.92 4698.3 -191.917 -1408.333333 270282.6389 36832.0069 1983402.78 3751.77 213232.59 895979.98 1983402.784 4 885 4113 958.92 4698.3 -73.9167 -585.3333333 43265.88889 5463.67361 342615.111 4333.77 48737.23 132910.00 342615.115 5 1156 4883 958.92 4698.3 197.0833 184.6666667 36394.72222 38841.8403 34101.7778 5670.38 619964.60 944871.44 34101.786 6 1146 5425 958.92 4698.3 187.0833 726.6666667 135947.2222 35000.1736 528044.444 5621.06 38438.26 851418.58 528044.447 7 892 4414 958.92 4698.3 -66.9167 -284.3333333 19026.63889 4477.84028 80845.4444 4368.29 2089.39 108928.50 80845.448 8 938 5506 958.92 4698.3 -20.9167 807.6666667 -16893.69444 437.506944 652325.444 4595.17 829612.83 10642.85 652325.449 9 769 3346 958.92 4698.3 -189.917 -1352.333333 256830.6389 36068.3403 1828805.44 3761.64 172752.82 877402.93 1828805.44

10 10 677 3673 958.92 4698.3 -281.917 -1025.333333 289058.5556 79477.0069 1051308.44 3307.88 133314.47 1933367.56 1051308.4411 11 1174 6542 958.92 4698.3 215.0833 1843.666667 396541.9722 46260.8403 3399106.78 5759.16 612843.09 1125346.95 3399106.7812 12 1009 5088 958.92 4698.3 50.08333 389.6666667 19515.80556 2508.34028 151840.111 4945.35 20348.47 61018.20 151840.11

Sum 11507 56380 4.55E-13 3.63798E-12 1488360.333 301766.917 10929176.7 56380 3588357.12 7340819.55 10929176.67Average 958.92 4698 SQRT 549.33 3305.93Observns 12

Correlation Coefficient 0.8196

Coefficient of Determination 0.6717

Variations Explained

= (Corelation Coeff)2 0.6717 67.17%Y' = a + bXb (Slope) 4.9322 Standard Error 599.0290

a (intercept) -31.1895

Multiple Variable Regression

• Demand (Y) is dependent on 2 or more independent variables (Price X1, Income X2)

• No relation between Price (X1) and Income (X2)

Inter Fuel Substitution

Dependent Variable

• Demand of Naptha (Y)

• Y = -9.3X1 + 30.3

• Y = -4X1 -0.8X2 + 15.5

• Y = -3.95X1 -0.4X2 + 1X3 +1.56

• Y = -3.9X1 -0.35X2 + 0.98X3 + 0.21X4 + 1.2

• Secondary Data used

Independent Variables

• Natural Gas Sale (X1)

• Naptha Price (X2)

• Furnace Oil Sale (X3)

• Furnace Oil Price (X4)• Naptha Price and Naptha

Demand has negative relationship

• Naptha Demand has inverse relationship with Gas Sale. Positive relationship with Furnace Oil and Furnace Oil Price

Multiple Regression Examples

• Y – Expected Travel Cost

• X1 – No of days on Road

• X2 – Distance Travelled in miles

• Y = $90 + $48.5X1 + $0.4X2

• 200 vouchers analyzed with r = 0.68

• Estimate John’s Travel cost 300 miles and 5 days.

• If John submits a bill for $685, will he get payment?

• Are there any other factors ? Comment

Student SAT Score 2 Year GPA

A 421 2.90

B 377 2.93

C 585 3.00

D 690 3.45

E 608 3.66

F 390 2.88

G 415 2.15

H 481 2.53

I 729 3.22

J 501 1.99

K 613 2.75

L 709 3.90

M 366 1.60

RegressionExample

EstimateGPAFor SAT Score 350&800

MultiVariable Regression Models

• Reliability of Regression Model can be increased by introducing 2 or more independent variables affecting demand and formulate a multivariate regression model

• Y = ao + a1X1 + a2X2 + …. + anXn

• Y = a + b1X1 + b2X2

• ΣY = Na + b1ΣX1 + b2ΣX2

• ΣX1Y = aX1 + b1ΣX12 + b2ΣX1X2

• ΣX2Y = aX2 + b1ΣX1X2 + b2ΣX22

• Std Devn Sy = SQRT{(ΣY2 – a ΣY – b1ΣX1Y-b2 ΣX2Y)/ n-k-1}

Multiple Variable Regression Example

• A firm produces and sells 2 products X1 and X2.

• Data for 5 years is available for Total Profit and units sold of X1 and X2.

• Calculate the contribution (b1) of X1 and (b2) X2 and Fixed Cost by Multiple Regression.

• Profit (Y) = b1X1 + b2X2 – FC

Year Sales of X1 Sales of X2 Profit

2007 12 16 192

2008 14 13 87

2009 10 11 (181)

2010 14 8 (216)

2011 16 10 (8)

Qty Qty ProfitX1 X2 Y X1Y Sq X1 X2Y Sq X2 X1*X212 16 192 2304 144 3072 256 19214 13 87 1218 196 1131 169 18210 11 -181 -1810 100 -1991 121 11014 8 -216 -3024 196 -1728 64 11216 10 -8 -128 256 -80 100 160

66 58 -126 -1440 892 404 710 756

Multiple RegressionY = A + BX1 + CX2

SUM Y = N*A + B*SUM X1 + C*SUM X2SUM X1Y = A*SUM X1 + B*SUM SqX1 + C*SUM X1X2SUM X2Y = A*SUM X2 + B*SUM X1X2 + C*SUM SqX2

-126 = 5A + 66B + 58C Eq 1-1440 = 66A + 892B + 756C Eq 2404 = 58A + 756B + 710C Eq 3

A = -1229.71, B = 38.45, C = 60.075

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.999673241R Square 0.999346589Adjusted R Square 0.998693179Standard Error 6.280605814Observations 5

ANOVAdf SS MS F Significance F

Regression 2 120659.908 60329.95399 1529.431112 0.000653411Residual 2 78.89201878 39.44600939Total 4 120738.8

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -1229.713615 26.74174571 -45.98479203 0.000472567 -1344.77406 -1114.65317 -1344.77406 -1114.65317X1 38.45774648 1.467263844 26.21051874 0.001452452 32.14461969 44.77087326 32.14461969 44.77087326X2 60.07511737 1.097156078 54.75530652 0.000333373 55.35443578 64.79579897 55.35443578 64.79579897

Multiple Regression

Econometric Models• It consists of a system of statistical equations that

interrelate the activities of different sectors in the economy and help to assess their impact on the demand for a product or service.

• Econometric models are used when causative factors used in a regression equation are interdependent.

• Used for Long Term Demand Estimation Modelling for the National Economy(example Steel)

Subjective Forecasting Methods• Rely on experience & opinions of people

inside or outside the organization.

• Employed when there is lack of time, data, or introduction of a new product

• Estimates survey: Pooling of estimates made by individual salesmen

• Delphi Method: Panel of experts respond to a questionnaire.

Estimates Survey• Individual Salesmen submit estimates of demand

in their areas for a future period.• These estimates are pooled at regional level and

adjusted for regional economic and demographic factors

• Regional estimates are combined at headquarters

• Drawbacks are : recent experiences influence, dominant personalities may divert from general consensus, lack of measure for any accuracy.

Sales Man

Sales Man

Sales Man

Sales Man

Sales Man

Zonal Level

Zonal Level

Zonal Level

Regional Level

Regional Level

National Level Estimates Survey

Delphi Method

• Panel of experts respond to a questionnaire about future demand.

• Individual estimates are summarised and returned to panel members for revision.

• Feedback allows arriving at a consensus

• Cost depends on panel composition and number of rounds made.

• Used for Technological Forecasting

Delphi Technique -

Time Series Forecasting Methods• Time series data refers to a set of values of some

variable (Demand) measured at equally spaced time intervals (Months, Quarters)

• Trend: long term growth or decline in the average level of demand

• Cyclical: business cycle - large deviation of actual demand values from those expected from a trend

• Seasonal: annually repetitive demand fluctuations caused by weather, tradition, festivals

• Random: irregular residual in the demand due to many complex random forces in environment

Time Series

• Total Demand D = T x S x C x R or

• Total Demand D = T + S + C + R

• T = Trend Component, S = Seasonal Component, C = Cyclical Component and R = Random Component

• Total Demand can be either a product or sum of all the above 4 components

Time Series

0

100

200

300

400

500

600

700

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

Quarter

De

man

d

Data exhibits long term increasing trend With seasonal fluctuations

Seasonal Indices for Time Series

• If Time Series is exhibiting quarterly seasonal fluctuations every year, seasonal indices are to be calculated.

• Tabulate the quarterly data• The Demand data is to be de-seasonalized by dividing the

quarterly data by the respective seasonal index.• The de-seasonalized data is used for estimating the trend

(by regression)• The de-seasonalized forecast for a future quarter is

multiplied by the respective seasonal index to get the seasonalized forecast.

• Refer the example

Steps for Isolating Components Time Series

• Seasonal Component

• Trend Component

• Cyclical Component

• Random

• Compute Seasonal Indices. Deseasonalize by dividing vales by seasonal indices

• Use Regression to fit the Trend with Deseasonalized Data

• Isolate Trend component and use Moving averages for Cylical Component

• Isolate Cylical and remaining is Random

Quarterly Sales, Lakh Rupees Annual

Year Q1 Q2 Q3 Q4 Total

2002 520 730 820 530 2600

2003 590 810 900 600 2900

2004 650 900 1000 650 3200

Total 1760 2440 2720 1780 8700

Average 586.67 813.33 906.67 593.33 725

Seasonal Index = Quarter Average/Total Quarter Average

Seasonal 0.81 1.12 1.25 0.82 4.00

Index

Deseasonalise by dividing by seasonal indices for each quarter

Year Q1 Q2 Q3 Q4 Total

2002 642.61 650.72 655.70 647.61 2596.64

2003 729.12 722.03 719.67 733.15 2903.96

2004 803.27 802.25 799.63 794.24 3199.40

Total 2175.00 2175.00 2175.00 2175.00 8700.00

8700/12 = 725

586.67/725 = 0.81

813.33/725 = 1.12

520/0.81 = 642.61

900/1.12 = 802.25

12 = 4Qtr x 3 yr

Deseasonalising is also termed as Normalisation

Year Quarter X Y=TSCR2002 Q1 1 289

Q2 2 410Q3 3 301Q4 4 213

2003 Q1 5 212Q2 6 371Q3 7 374Q4 8 333

2004 Q1 9 293Q2 10 441Q3 11 411Q4 12 363

2005 Q1 13 324Q2 14 462Q3 15 379Q4 16 301

2006 Q1 17 347Q2 18 520Q3 19 340Q4 20 521

2007 Q1 21 381Q2 22 594Q3 23 573Q4 24 504

2008 Q1 25 444Q2 26 592Q3 27 571Q4 28 507

Time Series Example

AnnualYear Q1 Q2 Q3 Q4 Total2002 289 410 301 213 12132003 212 371 374 333 12902004 293 441 411 363 15082005 324 462 379 301 14662006 347 520 340 521 17282007 381 594 573 504 20522008 444 592 571 507 2114

Total 2290 3390 2949 2742 11371Average 327.14 484.29 421.29 391.71 406.11

Seasonal 0.81 1.19 1.04 0.96 4.00Index

Year Q1 Q2 Q3 Q4 Total2002 358.76 343.81 290.16 220.83 1213.552003 263.17 311.11 360.53 345.24 1280.042004 363.72 369.81 396.19 376.34 1506.062005 402.21 387.42 365.34 312.06 1467.032006 430.76 436.06 327.75 540.14 1734.712007 472.96 498.11 552.36 522.52 2045.952008 551.17 496.43 550.43 525.63 2123.66

Total 2842.75 2842.75 2842.75 2842.75 11371.00

Quarterly Sales, Lakh Rupees

Seasonal Index = Quarter Average/Total Quarter Average

Deseasonalise by dividing by seasonal indices for each quarter

Year Quarter Y=TSCR SI Y=TCR X XY X2

2005 Q1 289 0.81 358.76 1 358.76 1Q2 410 1.19 343.81 2 687.63 4Q3 301 1.04 290.16 3 870.47 9Q4 213 0.96 220.83 4 883.31 16

2003 Q1 212 0.81 263.17 5 1315.86 25Q2 371 1.19 311.11 6 1866.66 36Q3 374 1.04 360.53 7 2523.68 49Q4 333 0.96 345.24 8 2761.88 64

2004 Q1 293 0.81 363.72 9 3273.51 81Q2 441 1.19 369.81 10 3698.09 100Q3 411 1.04 396.19 11 4358.11 121Q4 363 0.96 376.34 12 4516.05 144

2005 Q1 324 0.81 402.21 13 5228.67 169Q2 462 1.19 387.42 14 5423.87 196Q3 379 1.04 365.34 15 5480.17 225Q4 301 0.96 312.06 16 4992.96 256

2006 Q1 347 0.81 430.76 17 7322.87 289Q2 520 1.19 436.06 18 7849.01 324Q3 340 1.04 327.75 19 6227.25 361Q4 521 0.96 540.14 20 10802.86 400

2007 Q1 381 0.81 472.96 21 9932.25 441Q2 594 1.19 498.11 22 10958.42 484Q3 573 1.04 552.36 23 12704.17 529Q4 504 0.96 522.52 24 12540.45 576

2008 Q1 444 0.81 551.17 25 13779.27 625Q2 592 1.19 496.43 26 12907.26 676Q3 571 1.04 550.43 27 14861.54 729Q4 507 0.96 525.63 28 14717.61 784

Total 11371 11371.00 406.00 182842.62 7714.00

Y = 9.83X + 263.54

11371 = 28A + 406B182843 = 406A + 7714B

A = 263.54, B = 9.83

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Series1

Seasonalised Data

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Series1

Deseasonalized Data

Trend T Cyclical RandomYear Quarter X Y=TSCR SI Y=TCR Y=9.83X+263.54 Y=CR C R2002 Q1 1 289 0.81 358.76 273.37 1.31

Q2 2 410 1.19 343.81 283.20 1.21 1.17 1.04Q3 3 301 1.04 290.16 293.03 0.99 0.98 1.01Q4 4 213 0.96 220.83 302.86 0.73 0.85 0.85

2003 Q1 5 212 0.81 263.17 312.69 0.84 0.85 1.00Q2 6 371 1.19 311.11 322.52 0.96 0.96 1.00Q3 7 374 1.04 360.53 332.35 1.08 1.02 1.06Q4 8 333 0.96 345.24 342.18 1.01 1.04 0.97

2004 Q1 9 293 0.81 363.72 352.01 1.03 1.02 1.01Q2 10 441 1.19 369.81 361.84 1.02 1.04 0.98Q3 11 411 1.04 396.19 371.67 1.07 1.02 1.04Q4 12 363 0.96 376.34 381.50 0.99 1.03 0.96

2005 Q1 13 324 0.81 402.21 391.33 1.03 0.99 1.03Q2 14 462 1.19 387.42 401.16 0.97 0.96 1.01Q3 15 379 1.04 365.34 410.99 0.89 0.87 1.03Q4 16 301 0.96 312.06 420.82 0.74 0.88 0.85

2006 Q1 17 347 0.81 430.76 430.65 1.00 0.91 1.10Q2 18 520 1.19 436.06 440.48 0.99 0.91 1.09Q3 19 340 1.04 327.75 450.31 0.73 0.96 0.76Q4 20 521 0.96 540.14 460.14 1.17 0.97 1.21

2007 Q1 21 381 0.81 472.96 469.97 1.01 1.07 0.94Q2 22 594 1.19 498.11 479.80 1.04 1.06 0.98Q3 23 573 1.04 552.36 489.63 1.13 1.07 1.05Q4 24 504 0.96 522.52 499.46 1.05 1.09 0.96

2008 Q1 25 444 0.81 551.17 509.29 1.08 1.03 1.05Q2 26 592 1.19 496.43 519.12 0.96 1.03 0.93Q3 27 571 1.04 550.43 528.95 1.04 0.99 1.05Q4 28 507 0.96 525.63 538.78 0.98

Total 11371 11371.00 11370.10

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Mean = 0.99

Cyclical Graph (Y=CR vs Quarters)

Quarters

Measurement & Control of Forecast Errors

• Forecast is incomplete without an estimate of the expected error.

• Mean Squared Error (MSE) = Sum of Squared Errors/Number of Periods

• Mean Absolute Deviation (MAD) = Sum of Absolute Errors/Number of Periods

• Tracking Signal = Running sum of forecast Errors/Mean Absolute Deviation

Summary

• Forecasting provides vital information for any future activity

• Estimates of Demand cover quantity, timing, locations, quality

• Long, Intermediate, Short Term Forecasts• Cost Benefits • Forecasting Methods – Predictive, Causal, Time Series,

Moving Averages, Exponential Smoothing• Forecast error – Idle resources or shortages• Forecasting is more as an art rather than a science