Evans Analytics2e Ppt 09

7/23/2019 Evans Analytics2e Ppt 09

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Chapter 9

ForecastingTechniques


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Managers require good forecasts of future events. Business Analysts may choose from a wide range

of forecasting techniques to support decisionmaking.

Three major categories of forecasting approaches:

1. ualitative and judgmental techniques

!. "tatistical time#series models

$. %&planatory'causal models

Forecasting Techniques


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ualitative and (udgmental techniques rely one&perience and intuition.

They are necessary when historical data is notavaila)le or when predictions are needed far into the

future. The historical analogy approach o)tains a forecast

through comparative analysis with prior situations. The Delphi method questions an anonymous panel

of e&perts !#$ times in order to reach a convergenceof opinion on the forecasted varia)le.

Qualitative and Judgmental Forecasting


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%arly 1*++ , oil price was a)out -!! a )arrel Mid#1*++ , oil price dropped to -11 a )arrel

)ecause of oversupply high production in non#

/0% regions and lower than normal demand 2n the past /0% would raise the price of oil. 3istorical analogy would forecast a higher price. 3owever the price continued to drop even though

/0% agreed to cut production. 3istorical analogies cannot always account for

current realities4

Example 9.1 !redicting the !rice o" #il


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$ndicatorsare measures that are )elieved toinfluence the )ehavior of a varia)le we wish toforecast.

2ndicators are often com)ined quantitatively intoan index a single measure that weights multipleindicators thus providing a measure of overalle&pectation.

%&ample: 5ow (ones 2ndustrial Average

$ndicators and $ndexes


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650 76ross 5omestic 0roduct8 measures the value of allgoods and services produced. 650 rises and falls in a cyclic fashion.

9orecasting 650 is often done using leading indicators7series that change )efore the 650 changes8 andlaggingindicators7series that follow changes in the 6508indicators.

%&amples

eading-formation of )usiness enterprises # percent change in money supply 7M18 agging # )usiness investment e&penditures

# prime rate

# inventories on hand

Example 9.% Economic $ndicators


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AnIndex of Leading Indicators was developed )ythe 5epartment of ommerce.

This inde& is related to the economic performanceis availa)le from www.conference#)oard.org.

2t includes measures such as:# average weekly manufacturing hours# new orders for consumer goods# )uilding permits for private housing# ";0


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Time (eries, a stream of historical data such asweekly sales T> num)er of periods t> 1 ! ? T

Time series generally have components such as:

# random )ehavior # trends 7upward or downward8 # seasonal effects # cyclical effects (tationary time series have only random )ehavior.A trendis a gradual upward or downward movement

of a time series.

(tatistical Forecasting )odels


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TheEnergy Production & Consumption 6eneral upward trend with some short downward trends@

the time series is composed of several different shorttrends.

Example 9.* $denti"ying Trends in a Time

(eries


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A seasonal e""ect is one that repeats at fi&edintervals of time typically a year month week orday.

(easonal E""ects


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Cyclical e""ects descri)e ups and downs over a

much longer time frame such as several years.

Cyclical E""ects


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Moving average model %&ponential smoothing model

These are useful over short time periods when trend

seasonal or cyclical effects are not significant

Forecasting )odels "or (tationary

Time (eries


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The simple moving average method is asmoothing method )ased on the idea of averagingrandom fluctuations in the time series to identifythe underlying direction in which the time series ischanging.

The simple moving average forecast for the ne&tperiod is computed as the average of the most

recent ko)servations. arger values of kresult in smoother forecast models

since e&treme values have less impact.

)oving +verage )odels


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The Tablet Computer Salesdata contains the num)er ofunits sold over the past 1 weeks.

Three#period moving average forecast for week 1+:

Example 9., )oving +verage

Forecasting


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(preadsheet $mplementation o"

)oving +verage Forecasting


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Data nalysis options

Excel Moving Average Tool

e do notrecommend using thechart or error options)ecause the forecastsgenerated )y this tool

are not properlyaligned with the data


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"elect Smoot!ingfrom theTime Series group andselect "o#ing #erage

%nter the data range andmove the time varia)le anddependent varia)le to the)o&es on the right. %nter

the interval 7k8.

Example 9.- )oving +verage

Forecasting ithXLMiner


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$L"inerresults

Examnle 9.- Continued


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Mean a)solute

deviation 7MA58

Mean square error7M"%8

Coot mean squareerror 7CM"%8

Mean a)solutepercentage error7MA0%8

Error )etrics and Forecast +ccuarcy


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Tablet Computer Sales data !# $# and D#period moving average models !#period model ahs lowest error metric values

Example 9./ 0sing Error )etrics to

Compare )oving +verage Forecasts


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Exponential (moothing )odels

(imple exponential smoothing model:

where %t'is the forecast for time period tE 1 %tis the

forecast for period ttis the o)served value in period t

and is a constant )etween = and 1 called the

smoothing constant. To )egin set %'and %(equal to the actual o)servation in

period 1'.


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Example 9.9 0sing Exponential (moothing to

Forecast Tablet Computer Sales

9orecast for week $ when > =.: 71 , =.87++8 E 7=.87DD8 >


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Example 9.1 Finding the 2est Exponential

(moothing )odel "or Tablet Computer Sales

The forecast using > =.F provides the lowest error metrics.


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"electData nalysis from thenalysisgroup and thenchoose Exponential Smoot!ing

Gote that Damping factor ) 1 The first cell of the *utput +ange should )e adjacent to

the first data point

Example 9.11 0sing Excel3s Exponential

(moothing Tool


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Exponential Smoot!ing tool results

Example 9.11 Continued


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"elect Exponentialfrom the TimeSeries,Smoot!ingmenu.

ithin the eig!tspane it provides options toeither enter the smoothing constant Le#el .lp!a/or to check an *ptimi0e)o& which will find the

)est value of the smoothing constant.

Exponential (moothing inXLMiner


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Example 9.1% #ptimi4ing Exponential (moothing

Forecasts 0singXLMiner

The )estsmoothingconstant is=.F$


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Dou5le moving average and dou5le exponentialsmoothing

Based on the linear trend equation

The forecast for kperiods into the future is a function ofthe le#elat and the trend bt

The models differ in their computations of at and bt $L"inerdoes not support a procedure for dou)le

moving average@ however it does provide one for dou)lee&ponential smoothing.

Forecasting )odels "or Time (eries ith

a 'inear Trend


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%stimates of the parameters are o)tained fromthe following equations:

2nitial values are chosen for a'as'and b'as

(,'. %quation 7*.8 must then )e used to

compute atand btfor the entire time series to )ea)le to generate forecasts into the future.

Dou5le Exponential (moothing


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%&cel file Coal Production

Example 9.1& Dou5le Exponential

(moothing ithXLMiner


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$L"ineroptimiHationresults

the )estvalues of and are=.F+D and=.==

Example 9.1& Continued


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"imple linear regression can )e applied toforecasting using time as the independentvaria)le.

6egression72ased Forecasting "or

Time (eries ith a 'inear Trend


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Coal Productiondata with a linear trendline

Example 9.1* Forecasting 0sing

Trendlines

Gote that the linearmodel does notadequately predict therecent drop inproduction after !==+.


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hen autocorrelation is present successive

o)servations are correlated with one another@ fore&ample large o)servations tend to follow other largeo)servations and small o)servations also tend to followone another.

2n such cases other approaches called autoregressive modelsare more appropriate.

+utocorrelation in Time (eries


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hen time series e&hi)it seasonality differenttechniques provide )etter forecasts than the oneswe have descri)ed: Multiple regression models with categorical varia)les for

the seasonal components 3olt#inters models similar to e&ponential smoothing

models in that smoothing constants are used tosmooth out variations in the level and seasonalpatterns over time. 9or time series with seasonality )utno trend$L"iner supports a 3olt#inters method )utdoes not have the a)ility to optimiHe the parameters.

Forecasting Time (eries ith (easonality


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1as & Electric %&cel file Ise a seasonal categorical varia)le with k> 1! levels. onstruct the regression

model using k # 1 dummyvaria)les with (anuary)eing the reference month.

Example 9.1, 6egression72ased

Forecasting "or 8atural as 0sage


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5ata matri&

Example 9.1, Continued


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9inalregressionresults 7timeand 9e)ruary

wereinsignificant8

Example 9.1, Continued


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The :olt7;inters additive model applies to time series withrelatively sta)le seasonality and is )ased on the equation

The :olt7;inters multiplicative model applies to time serieswhose amplitude increases or decreases over time and is

A chart of the time series should )e viewed first to identify theappropriate type of model to use.

:olt7;inters )odels "or Forecasting

Time (eries ith (easonality and Trend


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$L"iner 2 Time Series 2

Smoot!ing 23olt inter 4o

Trend5

2n the Parameterspane the

value of Periodis the lengthof the season in this case1! months.

Jou will generally have toe&periment with the

smoothing constantstoidentify the )est model.

Example 9.1


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$L"inerresults

Example 9.1< Continued


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There is clearly a sta)le seasonal factor in the timeseries along with an increasing trend@ therefore the3olt#inters additive model would appear

Example 9.1- Forecasting New Car

Sales 0sing :olt7;inters )odels


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$L"iner 2 Time

Series 2 Smoot!ing 2

3olt inter dditi#e5

Example 9.1- Continued


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$L"inerresults

Example 9.1- Continued


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(electing +ppropriate Time7(eries72ased

Forecasting )ethods


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2n many forecasting applications otherindependent varia)les )esides time such aseconomic inde&es or demographic factors mayinfluence the time series.

%&planatory'causal models often calledeconometric models seek to identify factors thate&plain statistically the patterns o)served in thevaria)le )eing forecast usually with regressionanalysis

6egression Forecasting ith Causal

=aria5les


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%&cel file 1asoline Sales "imple trendline using week as the independent varia)le

Example 9.1/ Forecasting asoline

(ales 0sing (imple 'inear 6egression

0redicted sales for week 11 > +1!.**7118 E D*=.1 > 1$$$ gallons


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The average price per gallon changes each week andthis may influence consumer sales. Average price pergallon is a causal #ariable6

5evelop a multiple linear regression model to predict

gasoline sales using )oth time and price per gallon.

Example 9.19 $ncorporating Causal =aria5les in

a 6egression72ased Forecasting )odel


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Multiple regression model

Example 9.19 Continued

0redicted sales for week 11> !$$$ E 1


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(udgmental and qualitative methods are used forforecasting sales of product lines and )roadcompany and industry forecasts.

"imple time#series models are used for short# andmedium#range forecasts.

Cegression methods are typically used for long#term forecasts.

The !ractice o" Forecasting

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