Chapter 5: Demand Forecasting Department of Business Administration FALL 20 10 - 2011 I see that you will get an A this semester.

Chapter 5: Demand Forecasting

Department of Business Administration

FALL 2010-2011I see that you willget an A this semester.

2

Ch 5 : Demand Forecasting

© 2004, Managerial Economics, Dominick Salvatore © 2010/11, Sami Fethi, EMU, All Right Reserved.

Outline: What You Will Learn . . . List the elements of a good forecast. Outline the steps in the forecasting process. Describe at least three qualitative forecasting

techniques and the advantages and disadvantages of each.

Compare and contrast qualitative and quantitative approaches to forecasting.

Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems.

Describe two measures of forecast accuracy. Describe two ways of evaluating and controlling

forecasts. Identify the major factors to consider when choosing

a forecasting technique

3



What is meant by Forecasting and Why?What is meant by Forecasting and Why?

Forecasting is the process of estimating a variable, such as the sale of the firm at some future date.

Forecasting is important to business firm, government, and non-profit organization as a method of reducing the risk and uncertainty inherent in most managerial decisions.

A firm must decide how much of each product to produce, what price to charge, and how much to spend on advertising, and planning for the growth of the firm.

4



The aim of forecastingThe aim of forecasting

The aim of forecasting is to reduce the risk or uncertainty that the firm faces in its short-term operational decision making and in planning for its long term growth.

Forecasting the demand and sales of the firm’s product usually begins with macroeconomic forecast of general level of economic activity for the economy as a whole or GNP.

5



The aim of forecastingThe aim of forecasting

The firm uses the macro-forecasts of general economic activity as inputs for their micro-forecasts of the industry’s and firm’s demand and sales.

The firm’s demand and sales are usually forecasted on the basis of its historical market share and its planned marketing strategy (i.e., forecasting by product line and region).

The firm uses long-term forecasts for the economy and the industry to forecast expenditure on plant and equipment to meet its long-term growth plan and strategy.

6



Forecasting Process MapForecasting Process Map

MarketingMarketingSalesSalesProductProduct

Management Management & Finance& Finance

Executive Executive ManagementManagement

Production &Production & Inventory Inventory

ControlControl

Causal Causal FactorsFactors

Statistical Statistical ModelModel

Statistical Statistical ModelModel

Demand Demand HistoryHistory

Consensus Consensus ProcessProcess

Consensus Consensus ForecastForecast

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Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of ForecastsUses of Forecasts

8



Assumes causal systempast ==> future

Forecasts rarely perfect because of randomness

Forecasts more accurate forgroups vs. individuals

Forecast accuracy decreases as time horizon increases

I see that you willget an A this semester.

Features of ForecastsFeatures of Forecasts

9



Elements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

10



Steps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Obtain, clean and analyze data

Step 5 Make the forecast

Step 6 Monitor the forecast

“The forecast”

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Forecasting Techniques

A wide variety of forecasting methods are available to management. These range from the most naïve methodsnaïve methods that require little effort to highly complex approacheshighly complex approaches that are very costly in terms of time and effort such as econometric systems of simultaneous equations.

Mainly these techniques can break down into three parts: QQualitative approachesualitative approaches (Judgmental (Judgmental forecasts)forecasts) and QQuantitative approachesuantitative approaches (Time- (Time-series forecasts) and Associative model series forecasts) and Associative model forecasts)forecasts)..

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Judgmental - uses subjective inputs such as opinion from consumer surveys, sales staff etc..

Time series - uses historical data assuming the future will be like the past

Associative models - uses explanatory variables to predict the future

Forecasting TechniquesForecasting Techniques

13



Survey Techniques Some of the best-know surveys

Planned Plant and Equipment SpendingExpected Sales and Inventory ChangesConsumers’ Expenditure Plans

Opinion PollsBusiness ExecutivesSales ForceConsumer Intentions

Qualitative ForecastsQualitative Forecasts or or Judgmental ForecastsJudgmental Forecasts

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What are qualitative forecast ?

Qualitative forecast estimate variables at some future date using the results of surveys and opinion polls of business and consumer spending intentions.

The rational is that many economic decisions are made well in advance of actual expenditures.

For example, businesses usually plan to add to plant and equipment long before expenditures are actually incurred.

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Surveys and opinion pools are often used to make short-term forecasts when quantitative data are not available.

Usually based on judgments about causal factors that underlie the demand of particular products or services.

Do not require a demand history for the product or service, therefore are useful for new products/services.

Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events.

The approach/method that is appropriate depends on a product’s life cycle stage.


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Polls can also be very useful in supplementing quantitative forecasts, anticipating changes in consumer tastes or business expectations about future economic conditions, and forecasting the demand for a new product.

Firms conduct opinion polls for economic activities based on the results of published surveys of expenditure plans of businesses, consumers and governments.


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Survey Techniques– The rationale for forecasting based on surveys of economic intentions is that many economic decisions are made in advance of actual expenditures (Ex: Consumer’s decisions to purchase houses, automobiles, TV sets, furniture, vocation, education etc. are made months or years in advance of actual purchases)

Opinion Polls– The firm’s sales are strongly dependent on the level of economic activity and sales for the industry as a whole, but also on the policies adopted by the firm. The firm can forecast its sales by pooling experts within and outside the firm.


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Executive Polling- Firm can poll its top management from its sales, production, finance for the firm during the next quarter or year.

Bandwagon effect (opinions of some experts might be overshadowed by some dominant personality in their midst).

Delphi Method – experts are polled separately, and then feedback is provided without identifying the expert responsible for a particular opinion.


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Consumers intentions polling- Firms selling automobiles, furniture, etc.

can pool a sample of potential buyers on their purchasing intentions. By using results of the poll a firm can forecast its sales for different levels of consumer’s future income.

Sales force polling – – Forecast of the firm’s sales in each region

and for each product line, it is based on the opinion of the firm’s sales force in the field (people working closer to the market and their opinion about future sales can provide essential information to top management).


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Based on the assumption, the “forces” that generated the past demand will generate the future demand, i.e., history will tend to repeat itself.

Analysis of the past demand pattern provides a good basis for forecasting future demand.

Majority of quantitative approaches fall in the category of time series analysis.

Quantitative Forecasting Approaches

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Time Series Analysis

A time series (naive forecasting) is a set of numbers where the order or sequence of the numbers is important, i.e., historical demand

Attempts to forecasts future values of the time series by examining past observations of the data only. The assumption is that the time series will continue to move as in the past

Analysis of the time series identifies patterns Once the patterns are identified, they can be

used to develop a forecast

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Forecast Horizon

Short term Up to a year

Medium term One to five years

Long term More than five years

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Reasons for Fluctuations in Time Series Data

Secular Trend are noted by an upward or downward sloping line- long-term movement in data (e.g. Population shift, changing income and cultural changes).

Cycle fluctuations is a data pattern that may cover several years before it repeats itself- wavelike variations of more than one year’s duration (e.g. Economic, political and agricultural conditions).

Seasonality is a data pattern that repeats itself over the period of one year or less- short-term regular variations in data (e.g. Weekly or daily restaurant and supermarket experiences).

Irregular variations caused by unusual circumstances (e.g. Severe weather conditions, strikes or major changes in a product or service).

Random influences (noise) or variations results from random variation or unexplained causes. (e.g. residuals)

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Forecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Cycles

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Stable time series dataF(t) = A(t-1)

Seasonal variationsF(t) = A(t-n)

Data with trendsF(t) = A(t-1) + (A(t-1) – A(t-2))

Uses for Naïve ForecastsUses for Naïve Forecasts

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Techniques for Averaging

Moving average Weighted moving average Exponential smoothing

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Moving Averages

Moving average – A technique that averages a number of recent actual values, updated as new values become available.

Ft = MAn= n

At-n + … At-2 + At-1

Ft = WMAn=

wnAt-n + … wn-1At-2 + w1At-1

Weighted moving average – More recent values in a series are given more weight in computing the forecast.

nn=total amount of number of weights

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Simple Moving Average

35

37

39

41

43

45

47

1 2 3 4 5 6 7 8 9 10 11 12

Actual

MA3

MA5

Ft = MAn= n

At-n + … At-2 + At-1

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Simple Moving Average

An averaging period (AP) is given or selected The forecast for the next period is the arithmetic

average of the AP most recent actual demands It is called a “simple” average because each

period used to compute the average is equally weighted

It is called “moving” because as new demand data becomes available, the oldest data is not used

By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and high noise dampening)

By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and low noise dampening)

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Exponential SmoothingExponential Smoothing

Premise--The most recent observations might have the highest predictive value. Therefore, we should give more weight to the more recent time periods when forecasting.

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft = Ft-1 + (At-1 - Ft-1)Ft = forecast for period tFt-1 = forecast for the previous period smoothing constant At-1 = actual data for the previous period

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Exponential SmoothingExponential Smoothing ForecastsForecasts

The weights used to compute the forecast (moving average) are exponentially distributed.

The forecast is the sum of the old forecast and a portion (a) of the forecast error (A t-1 - Ft-1).

The smoothing constant, , must be between 0.0 and 1.0.

A large provides a high impulse response forecast.

A small provides a low impulse response forecast.

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Example-Moving AverageExample-Moving Average

Central Call Center (CCC) wishes to forecast the number of incoming calls it receives in a day from the customers of one of its clients, BMI. CCC schedules the appropriate number of telephone operators based on projected call volumes.CCC believes that the most recent 12 days of call volumes (shown on the next slide) are representative of the near future call volumes.

33



Moving Average Use the moving average method with an

AP = 3 days to develop a forecast of the call

volume in Day 13 (The 3 most recent demands)

compute a three-period average forecast compute a three-period average forecast given scenario above:given scenario above:

F13 = (168 + 198 + 159)/3 = 175.0 calls

Example-Moving AverageExample-Moving Average

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Example-Weighted Moving AverageExample-Weighted Moving Average

Weighted Moving Average (Central Call Center ) Use the weighted moving average method with an AP = 3 days and weights

of .1 (for oldest datum), .3, and .6 to develop a forecast of the call volume in Day 13.

compute a weighted average forecast given scenario above:compute a weighted average forecast given scenario above:

F13 = .1(168) + .3(198) + .6(159) = 171.6 calls

Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

1

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Example-Example-Exponential SmoothingExponential Smoothing Exponential Smoothing Exponential Smoothing ((Central Call Center) SupposeSuppose a smoothing constant value of .25 is used and the a smoothing constant value of .25 is used and the

exponential smoothing forecast for Day 11 was 180.76 callsexponential smoothing forecast for Day 11 was 180.76 calls .. what is the exponential smoothing forecast for Day 13?what is the exponential smoothing forecast for Day 13?

F12 = 180.76 + .25(198 – 180.76) = 185.07F12 = 180.76 + .25(198 – 180.76) = 185.07 F13 = 185.07 + .25(159 – 185.07) = 178.55F13 = 185.07 + .25(159 – 185.07) = 178.55

Ft = Ft-1 + (At-1 - Ft-1)

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Example 2-Example 2-Exponential SmoothingExponential SmoothingPeriod Actual Alpha = 0.1 Error Alpha = 0.4 Error

1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Exponential Smoothing Exponential Smoothing (Actual (Actual Demand forecasting ) SupposeSuppose a smoothing constant value of . a smoothing constant value of .1010 is used and the exponential is used and the exponential

smoothing forecast for smoothing forecast for the previous periodthe previous period was was 42 units (actual 42 units (actual demand was 40 units).demand was 40 units).

what is the exponential smoothing forecast for what is the exponential smoothing forecast for the nextthe next periodsperiods?? FF33 = = 4242 + . + .1010((4040 – – 4242) = ) = 4141..88 FF44 = = 41.841.8 + . + .1010((4343 – – 41.841.8) = ) = 41.9241.92

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35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual

Example 2-Example 2-Exponential SmoothingExponential SmoothingGraphical presentationGraphical presentation

38



Trend Projection

The simplest form of time series is projecting the past trend by fitting a straight line to the data either visually or more precisely by regression analysis.

Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables.

In simple linear regression analysis there is only one independent variable.

If the data is a time series, the independent variable is the time period.

The dependent variable is whatever we wish to forecast.

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Linear Trend Equation

Ft = Forecast for period t t = Specified number of time

periods a = Value of Ft at t = 0 b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft

40



Trend Projection

Linear Trend:St = S0 + b t

b = Growth per time period Constant Growth Rate(Non-linear)

St = S0 (1 + g)t

g = Growth rate Estimation of Growth Rate

ln St = ln S0 + t ln (1 + g)

41



Trend Projection- Simple Linear Regression

Regression Equation This model is of the form:

Y = a + bX

Y = dependent variable (the value of time series to be forecasted for period t)

X = independent variable ( time period in which the time series is to be forecasted)

a = y-axis intercept (estimated value of the time series, the constant of the regression)

b = slope of regression line (absolute amount of growth per period)

42



Trend Projection- Calculating a and b

Constants a a and bb The constants aa and bb

are computed using the equations given:

Once the a a and b b values are computed, a future value of X can be entered into the regression equation and a corresponding value of Y (the forecast) can be calculated.

2

2 2

x y- x xya =

n x -( x)

2 2

xy- x yb =

n x -( x)

n

43



Trend Projection- Calculating a and b

Or If formula b is used first, it may be used formula a in the following format:

2 2

xy- x yb =

n x -( x)

n n

XbYa

44



Example 1 for Trend Projection-Electricity sales

Suppose we have the data show electricity sales in a city between 1997.1 and 2000.4. The data are shown in the following table. Use time series regression to forecast the electricity consumption (mn kilowatt) for the next four quarters.next four quarters.

Do not forget to use the formulae a and b

45



Example1 for Trend Projection

2 2

xy- x yb =

n x -( x)

n

2

2 2

x y- x xya =

n x -( x)

TP T Q sq ( T ) Q x T1997Q1 1 11 1 111997Q2 2 15 4 301997Q3 3 12 9 361997Q4 4 14 16 561998Q1 5 12 25 601998Q2 6 17 36 1021998Q3 7 13 49 911998Q4 8 16 64 1281999Q1 9 14 81 1261999Q2 10 18 100 1801999Q3 11 15 121 1651999Q4 12 17 144 2042000Q1 13 15 169 1952000Q2 14 20 196 2802000Q3 15 16 225 2402000Q4 16 19 256 304

x y sq x xy sq sum xsum 136 244 1496 2208 18496

a 11.9b 0.394118

46



Example1 for Trend Projection

Y = 11.90 + 0.394XY = 11.90 + 0.394X

Y17 = 11.90 + 0.394(17) = 18.60 in the first quarter of 2001Y17 = 11.90 + 0.394(17) = 18.60 in the first quarter of 2001Y18 = 11.90 + 0.394(18) = 18.99 in the second quarter of 2001Y18 = 11.90 + 0.394(18) = 18.99 in the second quarter of 2001Y19 = 11.90 + 0.394(19) = 19.39 in the third quarter of 2001Y19 = 11.90 + 0.394(19) = 19.39 in the third quarter of 2001Y20 = 11.90 + 0.394(20) = 19.78 in the fourth quarter of 2001Y20 = 11.90 + 0.394(20) = 19.78 in the fourth quarter of 2001

Note:Note: Electricity sales are expected to increase Electricity sales are expected to increase by 0.394 mn kilowatt-hours per quarter.by 0.394 mn kilowatt-hours per quarter.

47



Example 2 for Trend Projection

Estimate a trend line using regression analysis

Year

Time Period

(t)Sales

(y)

200320042005200620072008

123456

204030507065

tbby 10

Use time (t) as the independent variable:

48




The linear trend model is:

Sales trend

01020304050607080

0 1 2 3 4 5 6 7

Year

sale

s

YearTime

Period (t)

Sales (y)

200320042005200620072008

123456

204030507065

t 5714.9333.12y

(continued)

49




Forecast for time period 7:

Sales

01020304050607080

0 1 2 3 4 5 6 7

Year

sale

s

YearTime

Period (t)

Sales (y)

2003200420052006200720082009

1234567

204030507065??

(continued)

33.79

(7) 5714.9333.12y

50



Example for Trend Projection using-Non linear form

St = S0 (1 + g)t

Running the regression above in the form of logarithms: ln St = ln S0 + t ln (1 + g) to construct the equation which has coefficients a and b.

Antilog of 2.49 is 12.06 and Antilog of 0.026 is 1.026.

CoefficientsStandard Error t StatIntercept 2.486914 0.062793 39.60489T 0.026371 0.006494 4.060874

St = 12.06(1.026)t

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Example for Trend Projection using St = S0 (1 + g)t

S17= 12.06(1.026)17 = 18.66 in the first quarter of 2001

S18= 12.06(1.026)18 = 19.14 in the second quarter of 2001

S19= 12.06(1.026)19 = 19.64 in the third quarter of 2001

S20= 12.06(1.026)20= 20.15 in the fourth quarter of 2001

These forecasts are similar to those obtained by fitting a linear trend

52



Evaluating Forecast-Model Performance Accuracy

Accuracy is the typical criterion for judging the performance of a forecasting approach

Accuracy is how well the forecasted values match the actual values

Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in its forecasts and changes in the market may require reevaluation of the approach

Accuracy can be measured in several ways Standard error of the forecast (SEF) Mean absolute deviation (MAD) Mean squared error (MSE) Mean absolute percent error (MAPE) Root mean squared error (RMSE)

53



Forecast Accuracy

Error - difference between actual value and predicted value

Mean Absolute Deviation (MAD)Average absolute error

Mean Squared Error (MSE)Average of squared error

Mean Absolute Percent Error (MAPE)Average absolute percent error

Root Mean Squared Error (RMSE)Root Average of squared error

54



MAD, MSE, and MAPE

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

MAPE = Actual forecas

t

n

/ Actual)*100)

2( )t tA FRMSE

n

55



MAD, MSE and MAPE

MAD Easy to compute Weights errors linearly

MSE Squares error More weight to large errors

MAPE Puts errors in perspective

RMSE Root of Squares error More weight to large errors

56



Example-MAD, MSE, and MAPECompute MAD, MSE and MAP for the following data showing actual and the predicted numbers of account serviced.

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75MSE= 10.86

MAPE= 1.28

22/8=2.7576/8-1=10.86

10.26/8=1.28 %

57



Example: Central Call Center-Forecast Accuracy - MAD

Which forecasting method (the AP = 3 moving average or the a = .25 exponential smoothing) is preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)

58



MADMADMAMA = = 20.520.5//99 = = 2.272.27

Example: Central Call Center-Forecast Accuracy - MAD

MADMADEXPEXP = = 18.0/918.0/9= = 2.02.0

E E AP4AP4 = = 161-187.3=26.3161-187.3=26.3 EEEXP4EXP4 = = 161-186=25.0161-186=25.0

FF44MAMA = ( = (186186 + + 217217 + 159)/3 = + 159)/3 = 187187..3333 calls calls

FF44EXPEXP = 18 = 1866 + .25( + .25(186186 – 18 – 1866) = ) = 186186..00 00 callscalls

59



Example-For MA TechniquesElectricity sales data from 2000.1 to 2002.4 (t=12)-Forecast

Accuracy - RMSE1 2 3 4 5 6 7 8

Quarter Firm's ams (A) Tqmaf (F) A-F sq(A-F) Fqmaf (F) A-F sq(A-F)1 202 223 234 24 21.6666667 2.333333 5.4444445 18 23 -5 256 23 21.6666667 1.333333 1.777778 21.4 1.6 2.567 19 21.6666667 -2.66667 7.111111 22 -3 98 17 20 -3 9 21.4 -4.4 19.369 22 19.6666667 2.333333 5.444444 20.2 1.8 3.2410 23 19.3333333 3.666667 13.44444 19.8 3.2 10.2411 18 20.6666667 -2.66667 7.111111 20.8 -2.8 7.8412 23 21 2 4 19.8 3.2 10.24

total 78.33333 total 62.4813 21.3333333 20.6

AP = 3 moving average AP = 5 moving average

60



Example-For MA TechniquesElectricity sales data from 2000.1 to 2002.4 (t=12)-Forecast

Accuracy - RMSE

2( )t tA FRMSE

n

RMSE for 3-qma=2.95

RMSE for 5-qma=2.99

Thus three-quarter moving average forecast is marginally better than the corresponding five- moving average forecast.

Sqroot of 78.33/9=2.95

Sqroot of 62.48/7=2.98

61



Example-Exponential Smoothing Example-Exponential Smoothing Forecast Accuracy - Forecast Accuracy - RMSERMSE1 2 3 4 5 6 7 8

QuarterFirm's ams (A) (F) w=0.3 A-F sq(A-F) (F) w=0.5 A-F sq(A-F)1 20 21 -1 1 21 -1 12 22 20.7 1.3 1.69 20.5 1.5 2.253 23 21.09 1.91 3.6481 21.25 1.75 3.06254 24 21.663 2.337 5.461569 22.125 1.875 3.5156255 18 22.3641 -4.3641 19.04537 23.0625 -5.0625 25.628916 23 21.05487 1.94513 3.783531 20.53125 2.46875 6.0947277 19 21.63841 -2.63841 6.961202 21.76563 -2.76563 7.6486828 17 20.84689 -3.84689 14.79853 20.38281 -3.38281 11.443429 22 19.69282 2.30718 5.323078 18.69141 3.308594 10.9467910 23 20.38497 2.615026 6.838359 20.3457 2.654297 7.04529211 18 21.16948 -3.16948 10.04562 21.67285 -3.67285 13.4898412 23 20.21864 2.781363 7.735978 19.83643 3.163574 10.0082

total 87.19 total 101.513 21 21.5

F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5

(20+22+...23)/12=21=F1

1 (1 )t t tF wA w F

62



Example-Exponential Smoothing Example-Exponential Smoothing Forecast Accuracy - Forecast Accuracy - RMSERMSE

F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3

F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5

RMSE with w=0.3 is 2.70 RMSE with w=0.5 is 2.91

Both exponential forecasts are better than the previous techniques in terms of average values.

2( )t tA FRMSE

n

63



Seasonal Variation

64



Seasonal Variation

Ratio to Trend Method

ActualTrend Forecast

Ratio =

SeasonalAdjustment =

Average of Ratios forEach Seasonal Period

AdjustedForecast =

TrendForecast

SeasonalAdjustment

65



Seasonal Variation

Ratio to Trend Method:Example Calculation for Quarter 1

Trend Forecast for 2001.1 = 11.90 + (0.394)(17) = 18.60

Seasonally Adjusted Forecast for 2001.1 = (18.60)(0.887) = 16.50

YEAR Forecasted Actual Act/Forec1997Q1 12.29 11 0.8950371998Q1 13.87 12 0.8651771999Q1 15.45 14 0.9061492000Q1 17.02 15 0.881316

AV 0.886920.887

Deseasonalize data=actual sales/seasonal relative (index)

66



Seasonal Variation

Select a representative historical data set. Develop a seasonal index for each season. Use the seasonal indexes to deseasonalize the

data. Perform linear regression analysis on the

deseasonalized data. Use the regression equation to compute the

forecasts. Use the seasonal indexes to reapply the

seasonal patterns to the forecasts.

67



Example: Computer Products Corp. Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly

forecasts of sales revenue for CPC’s line of Epsilon Computers. The analyst believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales. Calculate the seasonal indexes

68



Example: Computer Products Corp.

69



Example: Computer Products Corp.

70



Unseasonalized vs. Seasonalized

QuarterSeasonalized

SalesSeasonal

IndexDeseasonalized

Sales

123456789

1011…

2340252732483337375040

0.8251.3100.9200.9450.8251.3100.9200.9450.8251.3100.920 …

27.8830.5327.1728.5738.7936.6435.8739.1544.8538.1743.48

…

0.825

2327.88

Sales: Unseasonalized vs. Seasonalized

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11Quarter

Sale

s

Sales Deseasonalized Sales

71



Deflating a Time Series

Observed values can be adjusted to base year equivalent

Allows uniform comparison over time Deflation formula:

)100(I

yy

t

tadjt

where

= adjusted time series value at time t

yt = value of the time series at time t

It = index value at time t

tadjy

72



Deflating a Time Series: Example

Which movie made more money (in real terms)?

YearMovieTitle

Total Gross $

1939Gone With the Wind

199

1977 Star Wars 461

1997 Titanic 601

(Total Gross $ = Total domestic gross ticket receipts in $millions)

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Deflating a Time Series: Example

YearMovieTitle

Total Gross

CPI (base year =

1984)

Gross adjusted to 1984 dollars

1939Gone

With the Wind

199 13.9 1431.7

1977Star Wars

461 60.6 760.7

1997 Titanic 601 160.5 374.5

7.1431)100(9.13

199GWTW 1984adj

GWTW made about twice as much as Star Wars, and about 4 times as much as Titanic when measured in equivalent dollars

74



Barometric Methods

National Bureau of Economic Research Department of Commerce Leading Indicators Lagging Indicators Coincident Indicators Composite Index Diffusion Index

75



Barometric Methods

As conducted today, is primarily the result of the work conducted at the National Bureau of Economic Research (NBER) and the Conference Board.

Leading economic indicators – is used to forecast an increase in general business activity, and vice versa. (Ex: an increase in building permits can be used to forecast an increase in housing construction)

When some time series move in step or coincide with movements in general economic activity are called coincident indicators

Indicators which follow or lag movements in economic activity and are called lagging indicators

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Average weekly hours, manufacturing

Initial claims for unemployment insurance, thousands

Manufacturers’ new orders, consumer goods and materials

Vendor performance, slower deliveries diffusion index

Manufacturers’ new orders, nondefense capital goods

Building permits, new private housing units

Stock prices, 500 common stocks

Money supply, M2

Interest rate spread, 10-year Treasury bonds less federal funds

Index of consumer expectations

Leading indicators (10 series)

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Coincident indicators (4 series)

Employees on nonagricultural payrolls

Personal income less transfer payments

Industrial production

Manufacturing and trade sales

Lagging indicators (7 series)

Average duration of unemployment, weeks

Ratio, manufacturing and trade inventories to sales

Change in labor cost per unit of output, manufacturing

Average prime rate charged by banks

Commercial and industrial loans outstanding

Ratio, consumer installment credit to personal income

Change in consumer price index for services

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79



Econometric Models

The characteristic that distinguishes econometric model from other forecasting methods is that they seek to identify and measure the relative importance (elasticity) of the various determinants of demand or other economic variables to be forecasted.

Econometric forecasting frequently incorporates or uses the best features of other forecasting techniques, such as trend and seasonal variations, smoothing techniques, and leading indicators

80



Econometric Models

Single Equation Model of the Demand For Cereal (Good X)

QX = a0 + a1PX + a2Y + a3N + a4PS + a5PC + a6A + e

QX = Quantity of X

PX = Price of Good X

Y = Consumer Income

N = Size of Population

PS = Price of Muffins

PC = Price of Milk

A = Advertising

e = Random Error

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Econometric Models

Multiple Equation Model of GNP

1 1 1t t tC a bGNP u

2 2 1 2t t tI a b u

t t t tGNP C I G

2 11 21

1 11 1 1t t

t

b Ga aGNP b

b b

Reduced Form Equation

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Example-Econometric Models

Suppose we have the following equation and the estimated results for air travel between the USA and Europe from 1965 to 1978:

Q= 2.737-1.247 ln Pt + 1.905 ln GNPt

Q is number of passengers per year traveling between the two continents.

Pt is the average yearly air fare GNPt is U.S gross national product Suppose the estimated Pt+1 and GNPt+1 in 1979 are

$ 550 and $ 1480 respectively. Forecast the number of passengers in 1979.

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Example-Econometric Models

Qt+1= 2.737-1.247 (antilog of 550) + 1.905 (antilog of 1480)

= 2.737-1.247 (6.310) + 1.905 (7.300)=8.775

The antilog of 8.775= 6,470,000 passengers for 1979

The accuracy of the forecast depends on the accuracy of estimated demand coefficients and the estimated values of both the independent and explanatory variables in the demand equation.

84



Thanks

The EndThe End

Chapter 5: Demand Forecasting Department of Business Administration FALL 20 10 - 2011 I see that you will get an A this semester.

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