©2003 thomson/south-western 1 chapter 17 – quantitative business forecasting slides prepared by...

©2003 Thomson/South-Western 1

Chapter 17 –Chapter 17 –

Quantitative Quantitative Business Business ForecastingForecasting

Slides prepared by Jeff Heyl, Lincoln UniversitySlides prepared by Jeff Heyl, Lincoln University©2003 South-Western/Thomson Learning™

Introduction toIntroduction to Business StatisticsBusiness Statistics, 6e, 6eKvanli, Pavur, KeelingKvanli, Pavur, Keeling


Quantitative ForecastingQuantitative Forecasting

Regression ModelsRegression Models Time Series ModelsTime Series Models


Sales for Clayton Corp.Sales for Clayton Corp.

400 400 –

300 300 –

200 200 –

100 100 –

Forecast Forecast 350 350

Sal

esS

ales

(th

ou

san

ds

of

un

its)

(th

ou

san

ds

of

un

its)

• •

• • •

•• ••••

•• •

• ••

tt (time) (time)

Forecast periodForecast period((tt = 16) = 16)

| || | ||||||||||||

19881988 19911991 19961996 20032003

20022002

((tt = 1) = 1) ((tt = 15) = 15)DataData

Figure 17.1Figure 17.1


Procedure for Procedure for Forecasting with Forecasting with Time Series DataTime Series Data

Identification ofIdentification ofvariable of interestvariable of interest

Identification of differentIdentification of differentforecasting methodologiesforecasting methodologies

Estimation of modelEstimation of model

Calculation of forecastCalculation of forecastaccuracy and finalaccuracy and final

model selectionmodel selection

Generation of forecastsGeneration of forecasts

Reexamination of forecastingReexamination of forecastingaccuracy at a later timeaccuracy at a later time

Reexamination of presentReexamination of presentmodel or possible considerationmodel or possible considerationof alternate forecasting modelsof alternate forecasting models

Model selectionModel selectionand forecastingand forecasting

Model reviewModel review



Naive PredictorNaive Predictor



Time Series Containing Time Series Containing Trend and SeasonalityTrend and Seasonality

120 120 –

100 100 –

80 80 –

60 60 –

40 40 –

20 20 –Sal

es (

mill

ion

s o

f d

olla

rs)

Sal

es (

mill

ion

s o

f d

olla

rs)

ActualActualdata (ydata (y11))

DeseasonalizedDeseasonalizeddata (data (ddtt))

|

11|

22|

33|

44|

11|

22|

33|

44|

11|

22|

33|

44|

11|

22|

33|

44tt

19981998 19991999 20002000 20012001



Time SeriesTime SeriesTrend and SeasonalityTrend and Seasonality

Calculate the deseasonalized data Calculate the deseasonalized data from the original time seriesfrom the original time series

Construct a least squares line Construct a least squares line through the deseasonalized datathrough the deseasonalized data

Calculate the forecast for the time Calculate the forecast for the time period T+1period T+1


Video-Comp ExampleVideo-Comp Example

110 110 –100 100 –

90 90 –80 80 –70 70 –60 60 –50 50 –40 40 –30 30 –20 20 –10 10 –

|11

|22

|33

|44

|11

|22

|33

|44

|11

|22

|33

|44

|11

|22

|33

|44

tt = 1 = 1 tt = 16 = 16 20022002

|11

|22

ddtt = 19.372 + 5.037 = 19.372 + 5.037tt^̂ddtt dd1818

^̂

dd1717

^̂

tt

DeseasonalizedDeseasonalizeddata (data (ddtt))

Des

easo

nal

ized

dat

aD

esea

son

aliz

ed d

ata

(mil

lio

ns

of

do

llar

s)(m

illi

on

s o

f d

oll

ars)



Excel SolutionExcel Solution



Exponential SmoothingExponential Smoothing

This technique uses all the preceding This technique uses all the preceding observations to determine a smoothed observations to determine a smoothed value for a particular time periodvalue for a particular time period

SStt = smoothed value for time period, = smoothed value for time period, tt

= = AyAytt + (1 -+ (1 - A A))SStt-1-1 t t = 2, 3, 4, ...= 2, 3, 4, ...


Exponential SmoothingExponential Smoothing

YYtt

tt

No trendNo trend



Jefferson Civic CenterJefferson Civic Center

19891989 11 5.05.0 5.05.0 5.05.0 5.05.019901990 22 8.08.0 5.35.3 6.56.5 7.77.719911991 33 2.12.1 4.984.98 4.34.3 2.662.6619921992 44 7.17.1 5.195.19 5.75.7 6.666.6619931993 55 4.84.8 5.155.15 5.255.25 4.994.9919941994 66 2.02.0 4.844.84 3.623.62 2.302.3019951995 77 7.87.8 5.135.13 5.715.71 7.257.2519961996 88 5.05.0 5.125.12 5.365.36 5.235.2319971997 99 14.114.1 6.026.02 9.739.73 13.2113.2119981998 1010 13.013.0 6.726.72 11.3611.36 13.0213.0219991999 1111 13.513.5 7.397.39 12.4312.43 13.4513.4520002000 1212 14.214.2 8.078.07 13.3213.32 14.1214.1220012001 1313 14.014.0 8.678.67 13.6613.66 14.0114.01

YearYear tt YYtt SStt((AA = .1) = .1) SStt((AA = .5) = .5) SStt((AA = .9) = .9)

Table 17.1Table 17.1


Attendance ExampleAttendance Example

15 15 –

14 14 –

13 13 –

12 12 –

11 11 –

10 10 –

9 9 –

8 8 –

7 7 –

6 6 –

5 5 –

4 4 –

3 3 –

2 2 –

1 1 –

|19891989

|19911991

|19931993

|19951995

|19971997

|19991999

|20012001

tt

Av

era

ge

att

en

da

nc

e (

tho

us

an

ds

)A

ve

rag

e a

tte

nd

an

ce

(th

ou

sa

nd

s)

SStt((AA = .1) = .1)

SStt((AA = .5) = .5)

SStt((AA = .9) = .9)

Actual data (Actual data (yytt))



Forecasting Using Simple Forecasting Using Simple Exponential SmoothingExponential Smoothing



Forecasting Using Simple Forecasting Using Simple Exponential SmoothingExponential Smoothing


15 15 –

14 14 –

13 13 –

12 12 –

11 11 –

10 10 –

9 9 –

8 8 –

7 7 –

6 6 –

5 5 –

4 4 –

3 3 –

2 2 –

1 1 –|

19891989|

19911991|

19931993|

19951995|

19971997|

19991999|

20012001tt

Av

era

ge

att

en

da

nc

e (

tho

us

an

ds

)A

ve

rag

e a

tte

nd

an

ce

(th

ou

sa

nd

s)

yytt == S Stt-1-1

yytt

^̂


Linear Exponential Linear Exponential SmoothingSmoothing

SStt = = AyAytt + (1 - + (1 - A A)()(SStt - 1 - 1 + + bbtt - 1 - 1) ) tt = 2, 3, 4, ... = 2, 3, 4, ...

Smoothing ObservationsSmoothing Observations

bbtt = = BB((SStt - - SStt - 1 - 1) + (1 - ) + (1 - BB))bbtt - 1 - 1 tt = 2, 3, 4, ... = 2, 3, 4, ...

Smoothing TrendSmoothing Trend

yytt + 1 + 1 = = SStt + + bbtt t t = 1, 2, 3, ...= 1, 2, 3, ...^̂

yytt + + mm = = SStt + + mbmbtt t t = 1, 2, 3, ...= 1, 2, 3, ...^̂


Linear Exponential Linear Exponential SmoothingSmoothing

Procedure 2Procedure 2Use the first five years to estimate the Use the first five years to estimate the initial trendinitial trend

Procedure 1Procedure 1Let bLet b11 = 0= 0 provided you have a large provided you have a large

number of years, this procedure provides number of years, this procedure provides an adequate initial estimate for the trendan adequate initial estimate for the trend

Procedures for Summarizing the ResultsProcedures for Summarizing the Results


Summary for Linear Summary for Linear Exponential SmoothingExponential Smoothing



Predicted ValuesPredicted Values

YYtt

tt

500 500 –

400 400 –

300 300 –

200 200 –

100 100 –

|

11|

22|

44|

55|

66|

77|

88|

99|

1010|

33|

1111|

1212|

1414|

1515|

1616|

1717|

1818|

1919|

2020|

1313

Actual (Actual (yytt))

Procedure 1 (Procedure 1 (yytt))^̂




Exponential Smoothing for Exponential Smoothing for Trend and SeasonalityTrend and Seasonality

Winters’ MethodWinters’ Method

SStt = = AA + (1 - + (1 - AA)()(SStt - 1- 1 + + bbtt - 1 - 1))

FFtt = B = B + (+ (1 - B1 - B))FFt t - 1- 1

bbtt = C= C((SStt - - SSt t - 1- 1) + (1 -) + (1 - C C))bbt t - 1- 1

tt = = LL + 1, + 1, LL + 2, + 2, LL + 3, ... + 3, ...

yytt

FFtt - - LL

yytt

SStt


Forecasting Using Linear Forecasting Using Linear and Seasonal Exponential and Seasonal Exponential

SmoothingSmoothing

Procedure 1:Procedure 1:

3.3. Set the initial smoothed value for quarter Set the initial smoothed value for quarter 44 ((SS00) ) equal to the actual value for equal to the actual value for

quarter quarter 4 (4 (t t + 1)+ 1)

2.2. Set the initial trend estimate Set the initial trend estimate ((bb00)) equal to equal to 00

1.1. Set the initial seasonal factors equal to Set the initial seasonal factors equal to 11

yytt + + mm = ( = (SStt + + mbmbtt) • ) • FFtt + + mm - - LL^̂


Forecasting Using Linear Forecasting Using Linear and Seasonal Exponential and Seasonal Exponential

SmoothingSmoothingProcedure 2:Procedure 2:

3.3. The initial smoothed value for quarter 4, The initial smoothed value for quarter 4, SS00,, is the forecast value for each of the 4 is the forecast value for each of the 4

quarters in year t quarters in year t + 1+ 1

2. 2. Deseasonalize the data for the first two Deseasonalize the data for the first two years and calculate the least squares line years and calculate the least squares line through these deseasonalized values, dthrough these deseasonalized values, dtt

1.1. Use the first two years of data to determine Use the first two years of data to determine the seasonal indexesthe seasonal indexes


Jackson City ExampleJackson City Example



Jackson City ExampleJackson City Example


YYtt

tt

500 500 –

400 400 –

300 300 –

200 200 –

100 100 –

|

11|

22|

44|

55|

66|

77|

88|

99|

1010|

33|

1111|

1212|

1414|

1515|

1616|

1717|

1818|

1919|

2020|

1313

Actual (Actual (yytt))




Choosing the Appropriate Choosing the Appropriate Forecasting ProcedureForecasting Procedure

Exponential smoothing procedures are excellent Exponential smoothing procedures are excellent for short-term forecasts, whereas the component for short-term forecasts, whereas the component decomposition is useful for medium- and long-decomposition is useful for medium- and long-range forecastingrange forecasting

Short term forecast: one to three months Short term forecast: one to three months Medium-range forecast: four months to Medium-range forecast: four months to

two yearstwo years Long-range forecast: two or more yearsLong-range forecast: two or more years

Length of the forecastLength of the forecast


Comparing Predicted and Comparing Predicted and Observed ValuesObserved Values

There is no consensus among statisticians There is no consensus among statisticians as to which measure is preferableas to which measure is preferable

MAD (mean absolute deviation) MAD (mean absolute deviation) ==∑∑||eett||

nn

MAPE (mean absolute percentage error)MAPE (mean absolute percentage error) = =∑∑eett

22

nn

MSE (mean square error) MSE (mean square error) ==

∑∑eett

yytt

nn


Comparison of ProceduresComparison of Procedures

Method 1Method 1

MAD = 12/3 = 4.0MAD = 12/3 = 4.0

MSE = 48/3 = 16.0MSE = 48/3 = 16.0

MAPE = .295/3 = .098MAPE = .295/3 = .098

Method 2Method 2

MAD = 11/3 = 3.67MAD = 11/3 = 3.67

MSE = 57/3 = 19.0MSE = 57/3 = 19.0

MAPE = .260/3 = .087MAPE = .260/3 = .087

Table 17.6 (abbreviated)Table 17.6 (abbreviated)

©2003 thomson/south-western 1 chapter 17 – quantitative business forecasting slides prepared by...

Documents