SDA 3E Chapter 7

8/4/2019 SDA 3E Chapter 7

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2007 Pearson Education

Chapter 7: Forecasting


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Forecasting Techniques Qualitative and judgmental

Statistical time series models Explanatory/causal models


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Qualitative and Judgmental

Methods Historical analogy comparative

analysis with a previous situation

Delphi Method response to asequence of questionnaires by a panelof experts


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Indicators and Indexes Indicators measures believed to

influence the behavior of a variable we

wish to forecast Leading indicators

Lagging indicators

Index a weighted combination ofindicators

Indicators and indexes are often used ineconomic forecasting


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Time SeriesAtime series is a stream of historical

data

Components of time series

Trend

Short-term seasonal effects

Longer-term cyclical effects


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Example of a Time Series


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Statistical Forecasting Methods Moving average

Exponential smoothing

Regression analysis


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Simple Moving AverageAverage random fluctuations in a time

series to infer short-term changes in

directionAssumption: future observations will be

similar to recent past

Moving average for next period =average of most recent k observations


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Example: Moving Average

Forecast With k = 3


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Time Series Data and Moving

Averages


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Excel Tool: Moving Averages Tools > Data Analysis > MovingAverage

Enter range ofdata

Enter value of k

Select outputoptions

Select options


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Excel Results

Caution: chart aligns forecasts for next

period with current period data


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Weighted Moving Average Weight the most recent k observations,

with weights that add to 1.0

Higher weights on more recentobservations generally provide moreresponsive forecasts to rapidly changing

time series


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Error Metrics and Forecast

Accuracy Mean absolute

deviation (MAD)

Mean square error(MSE)

Mean absolutepercentage error

(MAPE)

n

FA

=MAD

n

1=i

tt

n

FA

=MSE

n

1=i

2

tt

n=MAPE

n

1=i

t

tt

A

FA


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Exponential Smoothing Exponential smoothing model:

Ft+1

= (1a)Ft

+ aAt

= Ft + a (AtFt) Ft+1 is the forecast for time period t+1,

Ft is the forecast for period t,

At is the observed value in period t, and a is a constant between 0 and 1, called the

smoothing constant.


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Excel Tool: Exponential

Smoothing Tools > Data Analysis > Exponential

Smoothing

Enter datarange

Dampingfactor = 1 - a

Select outputrange and

options


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Exponential Smoothing

Example


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Exponential Smoothing

Forecasts (a = 0.6)


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Forecasting Models With

Linear Trends Double Moving Average

Double Exponential Smoothing

Based on the linear trend equation

kbaFttkt


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Double Moving AverageMt= [ At-k+1+ At-k+2+ At]/k

Dt= [Mt-k+1 + Mt-k+2+ Mt]/k

at= 2MtDt

bt= (2/(k-1))[MtDt]

Use aT and bT in the linear trend equation to forecast kperiods beyond period T:

kbaFTTkT


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Example Calculations


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Double Moving Average

Forecasts


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Double Exponential Smoothingat=ayt+ (1-a) (at-1+ bt-1)

bt= (atat-1) + (1-)bt-1

Initialize: a1= A1b1= A2A1


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Forecasting Models With

SeasonalityAdditive model

Multiplicative model

ksttkt SaF

ksttkt SaF


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Additive Seasonality Level and seasonal factors:

Forecast for next period

at

= a( At

- St-s

) + (1-a) at-1

St= (At- at) + (1-) St-s

11

stttSaF


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Initialization

sA

s

t

t/

1

as=

at = as t = 1,2,s

St= A

t- a

tt = 1,2,s


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Example of Additive Seasonal

Model


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Models for Trend and

Seasonality Holt-Winters Additive Model

Holt-Winters Multiplicative Model


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Holt-Winters Additive Model Smoothing equations:

Forecast for period t + 1:

at=a ( At- St-s) + (1-a) (at-1+ bt-1)bt= (atat-1) + (1-)bt-1St= (At- at) + (1-) St-s

11

sttttSbaF


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Initializationbt= bs, for t = 1,2,s

bs= [ (As+1A1)/s + (As+2As)/s + .(As+sAs)/s] / s

Initial values for level and seasonal factors are the

same as in the additive seasonal model.


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CB Predictor Excel Add-In for forecasting


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CB Predictor Method Gallery


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CD Predictor Output: Methods

Table

Durbin-Watson statistic: check forautocorrelation; a value of 2indicates no autocorrelation

Theils U statistic: comparisonto nave forecast. U1, worse thanguessing


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CD Predictor Output: Results

Table


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CD Predictor Output: Chart

and Forecast Values


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Regression Trend Lines for

Forecasting


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Nonlinear Trend Line for

Forecasting


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Incorporating Seasonality into

Regression Models Use ordinal variables. Example:

Gas Usage = 0

+ 1

Time + 2

January + 3

February + 4

March + 5 April + 6 May + 7 June + 8 July + 9 August +

10 September + 11 October + 12 November

The forecast for December of the first year will

be 0 + 1(12). The forecast for January

(Time = 1) would be 0 + 1(1) + 2(1).


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Data Matrix


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Regression ANOVA Results


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Regression Forecast Results


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Causal Forecasting Models Causal models incorporate independent

variables such as economic indexes or

demographic factors that may influence thetime series.


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Model Sales = 0 + 1Week + 2 Price/Gallon

Sales = 39406.69 + 508.67 Week 16463.20

Price/Gallon

SDA 3E Chapter 7

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