Notes on Forecasting

7/25/2019 Notes on Forecasting

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2008 Prentice-Hall, Inc.

Chapter 5

To accompanyQuantitative Analysis for Management, Tenth Edition,by Render, Stair, and HannaPower Point slides created by Jeff Heyl

Forecasting

2009 Prentice-Hall, Inc. 2009 Prentice-Hall, Inc. 5 2

Introduction

!

Managers are always trying to reduceuncertainty and make better estimates of whatwill happen in the future

!

This is the main purpose of forecasting

!

Some firms use subjective methods

! Seat-of-the pants methods, intuition,experience

! There are also several quantitative techniques

!

Moving averages, exponential smoothing,trend projections, least squares regressionanalysis`

2009 Prentice-Hall, Inc. 5 3

Introduction

!

Eight steps to forecasting :

1. Determine the use of the forecastwhatobjective are we trying to obtain?

2. Select the items or quantities that are to beforecasted

3. Determine the time horizon of the forecast

4. Select the forecasting model or models

5. Gather the data needed to make theforecast

6. Validate the forecasting model

7. Make the forecast

8. Implement the results 2009 Prentice-Hall, Inc. 5 4

Introduction

! These steps are a systematic way of initiating,designing, and implementing a forecastingsystem

!

When used regularly over time, data is collectedroutinely and calculations performedautomatically

!

There is seldom one superior forecasting system

! Different organizations may use differenttechniques

!

Whatever tool works best for a firm is the onethey should use

! Assumptions

!

The future event is determined by the past.! Past data are available


Regression

Analysis

MultipleRegression

Moving

Average

ExponentialSmoothing

TrendProjections

Decomposition

Delphi

Methods

Jury of ExecutiveOpinion

Sales ForceComposite

ConsumerMarket Survey

Time-SeriesMethods

QualitativeModels

CausalMethods

Forecasting Models

ForecastingTechniques

Figure 5.1


Time-Series Models

! Time-series modelsattempt to predict thefuture based on the past

! Common time-series models are! Nave

!

Simple moving average and weighted movingaverage

!

Exponential smoothing

!

Trend projections

! Decomposition

! Regression analysis is used in trendprojections and one type of decompositionmodel


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Causal Models

!

Causal modelsuse variables or factorsthat might influence the quantity beingforecasted

! The objective is to build a model withthe best statistical relationship betweenthe variable being forecast and theindependent variables

! Regression analysis is the mostcommon technique used in causalmodeling


Qualitative Models

!

Qualitative modelsincorporate judgmentalor subjective factors

! Useful when subjective factors arethought to be important or when accuratequantitative data is difficult to obtain

! Common qualitative techniques are! Delphi method

! Jury of executive opinion

!

Sales force composite

!

Consumer market surveys


Qualitative Models

! Delphi Method an iterative group process where(possibly geographically dispersed) respondentsprovide input to decision makers

! Jury of Executive Opinion collects opinions of asmall group of high-level managers, possiblyusing statistical models for analysis

!

Sales Force Composite individual salespersonsestimate the sales in their region and the data iscompiled at a district or national level

! Consumer Market Survey input is solicited fromcustomers or potential customers regarding theirpurchasing plans


Scatter Diagrams

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 1 2

Time (Years)

AnnualSales

Radios

Televisions

CompactDiscs

Scatter diagrams are helpful when forecasting time-seriesdata because they depict the relationship between variables.


Scatter Diagrams

!

Wacker Distributors wants to forecast sales forthree different products

YEAR TELEVISION SETS RADIOS COMPACT DISC PLAYERS

1 250 300 110

2 250 310 100

3 250 320 1204 250 330 140

5 250 340 170

6 250 350 150

7 250 360 160

8 250 370 190

9 250 380 200

10 250 390 190

Table 5.1 2009 Prentice-Hall, Inc. 5 12

Scatter Diagrams

Figure 5.2

330

250

200

150

100

50

| | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

Time (Years)

AnnualSalesofTelevisions

(a)

!

Sales appear to beconstant over time

Sales = 250

!

A good estimate of

sales in year 11 is250 televisions


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Scatter Diagrams

! Sales appear to beincreasing at aconstant rate of 10radios per year

Sales = 290 + 10(Year)

!

A reasonableestimate of sales inyear 11 is 400radios

420

400

380

360

340

320

300

280

| | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

Time (Years)

AnnualSalesofRadios

(b)

Figure 5.2


Scatter Diagrams

! This trend line maynot be perfectlyaccurate becauseof variation fromyear to year

!

Sales appear to beincreasing

!

A forecast wouldprobably be alarger figure eachyear

200

180

160

140

120

100

| | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

Time (Years)

AnnualSalesofCDPlayers

(c)

Figure 5.2


Measures of Forecast Accuracy

!

We compare forecasted values with actual valuesto see how well one model works or to comparemodels

Forecast error = Actual value Forecast value

! One measure of accuracy is the mean absolutedeviation(MAD)

n

errorforecastMAD



!

Using a naveforecasting model

YEAR

ACTUALSALES OF CD

PLAYERS FORECAST SALES

ABSOLUTE VALUE OFERRORS (DEVIATION),(ACTUAL FORECAST)

1 110

2 100 110 |100 110| = 10

3 120 100 |120 100| = 20

4 140 120 |140 120| = 20

5 170 140 |170 140| = 30

6 150 170 |150 170| = 20

7 160 150 |160 150| = 10

8 190 160 |190 160| = 30

9 200 190 |200 190| = 10

10 190 200 |190 200| = 10

11 190

Sum of |errors| = 160

MAD = 160/9 = 17.8

Table 5.2



! Using a naveforecasting model

YEAR

ACTUALSALES OF CD

PLAYERS FORECAST SALES

ABSOLUTE VALUE OFERRORS (DEVIATION),(ACTUAL FORECAST)

1 110

2 100 110 |100 110| = 10

3 120 100 |120 110| = 20

4 140 120 |140 120| = 205 170 140 |170 140| = 30

6 150 170 |150 170| = 20

7 160 150 |160 150| = 10

8 190 160 |190 160| = 30

9 200 190 |200 190| = 10

10 190 200 |190 200| = 10

11 190

Sum of |errors| = 160

MAD = 160/9 = 17.8

Table 5.2

8179

160errorforecast.MAD

n



! There are other popular measures of forecastaccuracy

!

The mean squared error

n

2error)(

MSE

!

The mean absolute percent error

%MAPE 100actual

error

n

!

And biasis the average error and tells whether theforecast tends to be too high or too low and by

how much. Thus, it can be negative or positive.


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Ye ar Ac tu al C D Sa le s Fo re cas t S al es | Ac tu al -Fo re cas t|

1 110

2 100 110 10

3 120 100 20

4 140 120 20

5 170 140 30

6 150 170 20

7 160 150 10

8 190 160 30

9 200 190 10

10 190 200 10

11 190

Sum of |errors| 160

MAD 17.8


Hospital Days Forecast ErrorExample

Ms. Smith forecastedtotal hospital inpatientdays last year. Nowthat the actual data areknown, she isreevaluating herforecasting model.

Compute the MAD,MSE, and MAPE for herforecast.

Month Forecast ActualJAN 250 243

FEB 320 315

MAR 275 286

APR 260 256

MAY 250 241

JUN 275 298

JUL 300 292

AUG 325 333

SEP 320 326

OCT 350 378

NOV 365 382

DEC 380 396


Hospital Days Forecast ErrorExample

Forecast Actual |error| error2 |error/actual|

JAN 250 243 7 49 0.03

FEB 320 315 5 25 0.02

MAR 275 286 11 121 0.04

APR 260 256 4 16 0.02

MAY 250 241 9 81 0.04

JUN 275 298 23 529 0.08

JUL 300 292 8 64 0.03

AUG 325 333 8 64 0.02

SEP 320 326 6 36 0.02

OCT 350 378 28 784 0.07

NOV 365 382 17 289 0.04

DEC 380 396 16 256 0.04

AVERAGEMAD=11.83

MSE=192.83

MAPE=.0381*100 =3.81


Time-Series Forecasting Models

! A time series is a sequence of evenlyspaced events (weekly, monthly, quarterly,etc.)

! Time-series forecasts predict the futurebased solely of the past values of thevariable

! Other variables, no matter how potentiallyvaluable, are ignored


Decomposition of a Time-Series

!

A time series typically has four components

1.Trend(T) is the gradual upward ordownward movement of the data over time

2.Seasonality(S) is a pattern of demandfluctuations above or below trend line thatrepeats at regular intervals

3.Cycles(C) are patterns in annual data thatoccur every several years

4.Random variations(R) are blips in thedata caused by chance and unusualsituations


Decomposition of a Time-Series

Average Demandover 4 Years

TrendComponent

Actual

DemandLine

Time

DemandforPro

ductorService

| | | |

Year Year Year Year1 2 3 4

Seasonal Peaks

Figure 5.3


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Nave Forecast *

!

Nave forecast is the simplest technique. Ituses the actual demand for the past period asthe forecasted demand for the next period

! This makes the theory that the past will repeat.

! Also assumes that any time seriescomponents are either reflected in theprevious periods demand or do not exist.

Nave forecast, Ft+1 = Yt


Nave Forecast *

Period Actual Demand

1 35

2 40

3 55

4 65

5 60

6 -

Forecast

35

40

55

65

60


Moving Averages

! Moving averagescan be used when demand is relatively steadyover time

! The next forecast is the average of the most recent ndata valuesfrom the time series

! Conditions:

! There is a historical record of actual events.

! The forecast is based on a determined number of pastperiods.

! The past periods have equal importance.

! The most recent period of data is added and the oldest isdropped

!This methods tends to smooth out short-term irregularities inthe data series

n

nperiodspreviousindemandsofSumforecastaverageMoving


Moving Averages

! Mathematically

n

YYYF

nttt

t

11

1

...

where

= forecast for time period t+ 1

= actual value in time period t

n = number of periods to average

tY

1tF


Wallace Garden Supply Example

! Wallace Garden Supply wants toforecast demand for its Storage Shed

! They have collected data for the pastyear

!

They are using a three-month movingaverage to forecast demand (n= 3)



Table 5.3

MONTH ACTUAL SHED SALES THREE-MONTH MOVING AVERAGE

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14

January

(12 + 13 + 16)/3 = 13.67

(13 + 16 + 19)/3 = 16.00

(16 + 19 + 23)/3 = 19.33

(19 + 23 + 26)/3 = 22.67

(23 + 26 + 30)/3 = 26.33

(26 + 30 + 28)/3 = 28.00

(30 + 28 + 18)/3 = 25.33

(28 + 18 + 16)/3 = 20.67

(18 + 16 + 14)/3 = 16.00

(10 + 12 + 13)/3 = 11.67


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Weighted Moving Averages

!

Weighted moving averagesuse weights to putmore emphasis on recent periods

!

Often used when a trend or other pattern isemerging

)(

))((

Weights

periodinvalueActualperiodinWeight1

iF

t

! Mathematically

n

ntntt

twww

YwYwYwF

...

...

21

1121

1

where

wi= weight for the ithobservation


Weighted Moving Averages

!

Both simple and weighted averages areeffective in smoothing out fluctuations inthe demand pattern in order to providestable estimates

! Problems

!Increasing the size of nsmoothes outfluctuations better, but makes the methodless sensitive to real changes in the data

!

Moving averages can not pick up trendsvery well they will always stay within pastlevels and not predict a change to a higher orlower level



!

Wallace Garden Supply decides to try aweighted moving average model to forecastdemand for its Storage Shed

!

They decide on the following weightingscheme

WEIGHTS APPLIED PERIOD

3 Last month

2 Two months ago

1 Three months ago

6

3 x Sales last month + 2 x Sales two months ago + 1 X Sales three months ago

Sum of the weights



Table 5.4

MONTH ACTUAL SHED SALESTHREE-MONTH WEIGHTED

MOVING AVERAGE

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14

January

[(3 X 13) + (2 X 12) + (10)]/6 = 12.17

[(3 X 16) + (2 X 13) + (12)]/6 = 14.33

[(3 X 19) + (2 X 16) + (13)]/6 = 17.00

[(3 X 23) + (2 X 19) + (16)]/6 = 20.50

[(3 X 26) + (2 X 23) + (19)]/6 = 23.83

[(3 X 30) + (2 X 26) + (23)]/6 = 27.50

[(3 X 28) + (2 X 30) + (26)]/6 = 28.33

[(3 X 18) + (2 X 28) + (30)]/6 = 23.33

[(3 X 16) + (2 X 18) + (28)]/6 = 18.67

[(3 X 14) + (2 X 16) + (18)]/6 = 15.33


Exponential Smoothing

!

Exponential smoothingis easy to use andrequires little record keeping of data

!

It is a type of moving average

!

Conditions:! There is historical data of actual sales.

!

There is a historical record of past forecasts.! The smoothing constant is known.

New forecast = Last periods forecast+ (Last periods actual demand Last periods forecast)

Where is a weight (or smoothing constant) with avalue between 0 and 1 inclusive

A larger gives more importance to recent data whilea smaller value gives more importance to past data


Exponential Smoothing

!

Mathematically

)(tttt

FYFF 1

where

Ft+1

= new forecast (for time period t+ 1)

Ft= previous forecast (for time period t)

= smoothing constant (0 ! !1)

Yt= previous periods actual demand

!

The idea is simple the new estimate is theold estimate plus some fraction of the error inthe last period


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PM Computers: Data

Period Month Actual Demand

1 Jan 372 Feb 40

3 Mar 41

4 Apr 37

5 May 45

6 June 50

7 July 43

8 Aug 47

9 Sept 56

! Compute a 2-month moving average

! Compute a 3-month weighted average using weights of4,2,1 for the past three months of data

! Compute an exponential smoothing forecast using =0.7, previous forecast of 40

! Using MAD, what forecast is most accurate? 2009 Prentice-Hall, Inc. 5 49

PM Computers: Moving AverageSolution

2 month

MA A bs . Dev 3 mon th WMA A bs . Dev Exp. Sm. Ab s. De v

37.00

37.00 3.00

38.50 2.50 39.10 1.90

40.50 3.50 40.14 3.14 40.43 3.43

39.00 6.00 38.57 6.43 38.03 6.97

41.00 9.00 42.14 7.86 42.91 7.09

47.50 4.50 46.71 3.71 47.87 4.87

46.50 0.50 45.29 1.71 44.46 2.54

45.00 11.00 46.29 9.71 46.24 9.76

51.50 51.57 53.07

5.29 5.43 4.95MAD

Exponential smoothing resulted in the lowest MAD.


Trend Projection

! Trend projection fits a trend line to aseries of historical data points

! The line is projected into the future formedium- to long-range forecasts

! Several trend equations can bedeveloped based on exponential orquadratic models

! The simplest is a linear model developedusing regression analysis


Trend Projection

!

Trend projections are used to forecast time-series datathat exhibit a linear trend.

!

A trend line is simply a linear regression equationin which the independent variable (X) is the timeperiod

! The independent variable is the time period and thedependent variable is the actual observed value inthe time series.

!

Conditions:

!

There is historical data of actual sales.

!

There is an apparent linear trend in the figuresover time.


Trend Projection

! The mathematical form is: XbbY10

Where:

= predicted value

b0= intercept

b1= slope of the line

X= time period (i.e.,X= 1, 2, 3, ", n)

Y

b1= #xy nx y-------------

#x2 nx 2

b0= y b1x

Where:#= summation sign for n data points

x = values of independent variablesy= values of dependent variables

n = number of data points or observationsx = average of the values of the xs

y = average of the values of the ys 2009 Prentice-Hall, Inc. 5 56

Trend Projection

ValueofDependentVariable

Time

*

*

*

*

*

*

*Dist2

Dist4

Dist6

Dist1

Dist3

Dist5

Dist7

Figure 5.4


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Midwestern ManufacturingCompany Example

!

Midwestern Manufacturing Company hasexperienced the following demand for its electricalgenerators over the period of 2001 2007

YEAR ELECTRICAL GENERATORS SOLD

2001 74

2002 79

2003 80

2004 90

2005 105

2006 142

2007 122

Table 5.7Determine the forecast for 2008 and 2009, and

plot a time series. 2009 Prentice-Hall, Inc. 5 60


!

The forecast equation isXY 54107156 ..

! To project demand for 2008, we use the codingsystem to defineX= 8

(sales in 2008) = 56.71 + 10.54(8)= 141.03, or 141 generators

!

Likewise forX= 9

(sales in 2009) = 56.71 + 10.54(9)= 151.57, or 152 generators



GeneratorDemand

Year

160

150

140

130

120

110

100

90

80

70

60

50

| | | | | | | | |

2001 2002 2003 2004 2005 2006 2007 2008 2009

Actual Demand Line

Trend Line

XY 54107156 ..

Figure 5.5


Example 2

! The rated power capacity (inhrs/wk) over the past sixyears has been:

Alternative way to recode yearswhich simplifies math since #x = 0

Yr. Renum-bered

Yr., x

Capacity,

yX2 xy

1 -2.5 115 6.25 -287.25

2 -1.5 120 2.25 -180

3 -0.5 118 0.25 -59

4 +0.5 124 0.25 +62

5 +1.5 123 2.25 +183.5

6 +2.5 130 6.25 +325

# 0 730 17.5 45

Year RatedCapacity

(hrs/wk)

1 115

2 120

3 118

4 124

5 123

6 130

b1 = !xy/!x2= 5/17.5 = 2.57 b0 = !y/n= 730/6 = 121.67

y = 121.67 + 2.57x


Seasonal Variations

!

Recurring variations over time may indicate theneed for seasonal adjustments in the trend line

!

A seasonal index indicates how a particularseason compares with an average season

!

When no trend is present, the seasonal index

can be found by dividing the average value fora particular season by the average of all thedata

!

Conditions:! There is historical record of actual events.

! The past record of actual events is at least 2 years.

! There is an apparent trend in the figures over time.

! There is an apparent trend in the figures acrossseasons.


Seasonal Variations

! Eichler Supplies sells telephoneanswering machines

! Data has been collected for the past twoyears sales of one particular model

!

They want to create a forecast thatincludes seasonality


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Seasonal Variations

MONTH

SALES DEMANDAVERAGE TWO- YEAR

DEMANDMONTHLYDEMAND

AVERAGESEASONAL INDEXYEAR 1 YEAR 2

January 80 10090

94 0.957

February 85 7580

94 0.851

March 80 9085

94 0.904

April 110 90100

94 1.064

May 115 131123

94 1.309

June 120 110115

94 1.223

July 100 110105

94 1.117

August 110 90100

94 1.064

September 85 9590

94 0.957

October 75 8580

94 0.851

November 85 7580

94 0.851

December 80 8080

94 0.851

Total average demand = 1,128

Seasonal index =Average two-year demand

Average monthly demandAverage monthly demand = = 94

1,128

12 months

Table 5.8 2009 Prentice-Hall, Inc. 5 68

Seasonal Variations

! Suppose we expected the third year s annual demand for

answering machines to be 1,200 units, which is 100 permonth. We would not forecast each month to have a demandof 100, but we would ad- just these based on the seasonalindices as follows:

Jan. July96957012

2001

.

,

112117112

2001

.

,

Feb. Aug.85851012

2001.

,

106064112

2001.

,

Mar. Sept.90904012

2001.

,

96957012

2001.

,

Apr. Oct.106064112

2001.

,

85851012

2001.

,

May Nov.131309112

2001

.

,

85851012

2001

.

,

June Dec.122223112

2001.

,

85851012

2001.

,


Seasonal Variations with Trends

! When both trend and seasonal components are present in a timeseries, a change from one month to the next could be due to atrend, to a seasonal variation, or simply to random fluctuations.

! To help with this problem, the seasonal indices should becomputed using centered moving averageapproach whenevertrend is present.

! Using this approach prevents a variation due to trend from beingincorrectly interpreted as a variation due to the season.

! Conditions:! There is historical record of actual events.

! The past records of actual events is at least 2 years.

! There is an apparent trend in the figures over time.

! There is an apparent trend in the figures across seasons.

! There is a need to deseasonalize the projection for accuracy.


Steps Used to Compute SeasonalIndices based on CMAs

T T

.

:

. .

. .

.

. .

. .

. .

. .

. .

.

.

. .

.

.

. . .

. . .

. . .

. . .

..

CMA1quarter3 ofyear12 =0.511082 + 125 + 150 + 141 + 0.511162

4= 132.00

. .

. .

. .

. .

. .

. .

. .

. .

1. Compute a CMA for each observation (wherepossible)

2. Compute seasonal ratio = Observation/CMA forthat observation.

3. Average seasonal ratios to get seasonal indices.(This eliminates as much randomness aspossible.)

4. If seasonal indices do not add to the number ofseasons, multiply each index by (Number ofseasons)/(Sum of the indices).


Turner Industries Example



Seasonal Ratio =observation/CMA forthat observation

Average seasonal ratios toget seasonal indices.

Consider Q3. The actual sales in that quarterwere 150. To determine the magnitude of theseasonal variation, we should compare this

with an average quarter centered at that timeperiod. Thus, we should have a total of four

quarters (1 year of data) with an equal numberof quarters before and after quarter 3 so thetrend is averaged out. Thus, we need 1.5

quarters before quarter 3 and 1.5 quartersafter it. To obtain the CMA, we take quarters 2,

3, and 4 of year 1, plus one-half of quarter 1for year 1 and one-half of quarter 1 for year 2.


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Seasonal Ratio =observation/CMA forthat observation

Average seasonal ratios toget seasonal indices.


Scatter Plot of TurnerIndustries Sales and CMA


The Decomposition Method withTrend and Seasonal Components

!

Decomposition is the process of isolating lineartrend and seasonal factors to develop moreaccurate forecasts

!

The first step is to compute seasonal indices foreach season, then the data are deseasonalizedby dividing each number by its seasonal index

! A trend line is then found using thedeseasonalized data.


Steps to Develop a Forecast Usingthe Decomposition Method

1. Compute seasonal indices using CMAs.

2. Deseasonalize the data by dividingeach numberby its seasonal index.

3. Find the equation of a trend line using thedeseasonalizeddata.

4. Forecast the future periods using the trend line.

5. Multiplythe trend line forecast by theappropriate seasonal index


Deseasonalized Data forTurner Industries

T T

.

:

. .

. .

.

. .

. .

. .

. .

. .

.

.

. .

.

.

. . .

. . .

. . .

. . .

..

CMA1quarter3of year12 =0.511082 + 125 + 150 + 141 + 0.511162

4= 132.00

. .

. .

. .

. .

. .

. .

. .

. .


Finding the Trend Line ofDeseasonalized Data

b1= 2.34, b0= 124.78

Y = 124.78 + 2.34X where X = time

This equation is used to develop the forecast based on

trend, and the result is multiplied by the appropriate seasonalindex to make a seasonal adjustment.

The forecast for the first quarter of year 4 (time period = 13and seasonal index I1= 0.85)

Y = 124.78 + 2.34X = 124.78 + 2.34(13)= 155.2 (forecast before adjustment for seasonality)

Multiply this by the seasonal index for quarter 1:

Y x I1= 155.2 x 0.85 = 131.92

Find the forecast for quarters 2, 3 and 4 of the next year.


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Example 2

! Demand for Carriers mostpopular window airconditioner units is quiteseasonal. For each quarterof the past three years,demand has been asfollows:

! Find the seasonal indicesfor aircon demand.

! Use the seasoned indicesdeveloped anddeseasonalized the 12quarters of demand

Period Year Quarter Demand

1 1986 1 126

2 2 200

3 3 243

4 4 167

5 1987 1 132

6 2 211

7 3 243

8 4 167

9 1988 1 131

10 2 208

11 3 251

12 4 171


Example 3

! Del Monte Catsup wants toimprove the accuracy of theforecast by removing theeffect of seasonal trendbased on month in the t rendline formula. There is a lineartrend of the monthly salesover time with variation dueto the seasons based onmonth over the last 2 years.What is the forecast of themonthly sales next year?

Month Sales

Last Year This Year

Jan 6 8

Feb 11 15

Mar 15 17

Apr 16 16

May 15 16

Jun 25 23

Jul 21 20

Aug 24 25

Sep 24 28

Oct 19 21

Nov 20 28

Dec 25 29


Example 3 [Steps]

!Determine the seasonal index.

!Determine the deseasonalized sales.

!Determine the trend line formula.

!Determine the adjusted monthlysales forecast for next year.


MS Application-Forecasting:Taco Bell


Using The Computer to Forecast

! Spreadsheets can be used by small andmedium-sized forecasting problems

! More advanced programs (SAS, SPSS,Minitab) handle time-series and causalmodels

!

May automatically select best modelparameters

! Dedicated forecasting packages may befully automatic

! May be integrated with inventory planningand control


Question of the Day

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Notes on Forecasting