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Copyright © 2000 SAP AG. All rights reserved Accelerated SAP 08/21/98 1

Selecting the Right

ForecastingForecastingMethodMethod




2

Agenda

Tr aditional Sales For ecasting Methods Curr ent Sales For ecasting Methods and Techniques Being Used

Under lying Theor y of For ecasting Methods

Sales For ecasting Methodologies

Quantitative vs Qualitative

Tool Kit Appr oach

Build a Model

Components of Applied Market Response Modeling

Analyze an Actual Model Using Live Data

Intr oduction to Multi-Tier ed Causal Analysis

Composite For ecasting Application




3

Most companies seem to use simple techniques that ar e easy tocompr ehend and mostly those that involve judgment by companyemployees.

A method widely used r esults in for ecast goal-setting, this is not r eallyfor ecasting.

Her e companies begin their planning pr ocess with a cor por ate goal to incr ease sales by someper centage.

This tar get often comes dir ectly f r om the chief executive officer .

Then ever yone backs into their tar get based on what each business unit manager thinks they candeliver .

Finally, if they don¶t meet the tar get when totaled the CEO either assigns tar gets to par ticular business units or puts a financial plug in place hoping someone will over deliver .

Tr aditional Sales For ecasting Methods...




4

Curr ent Sales For ecasting Methods andTechniques Being Used

Mor e focus on utilizing time ser ies methods to pr edict baseline sales demand

Pr imar ily using Winter ¶s Exponential Smoothing

Also, some Decomposition/Census X-11

Ver y little ARIMA/Box-Jenkins

Judgmental techniques still seem to be the dominant method of choice

Sales For ce Composites

Jur y of Executive Opinion

Delphi Appr oach

Multiple Regr ession is beginning to be utilized

Mor e Univer sities ar e teaching Regr ession Applications

Accessing causal data is becoming easier

Regr ession is r equir ed to evaluate and pr edict sales pr omotions




5

Under lying Theor y of For ecasting Methods...




6

For ecast = Patter n + Randomness





7



This simple equation is r eally saying that when the aver agepatter n of the under lying data has been identified somedeviation will occur between the for ecasting method appliedand the actual occurr ence.




8






9

Sales For ecasting Methods...




10

Two Types Of Sales For ecasting Methodologies

Qualitative

Also Known as ³Judgmental´ or Subjective

Quantitative Also known as ³Mathematical´ or Objective




11

Ar e also known as Judgmental

Rely on subjective assessments of a per son or gr oup of people

Using intuitive or gut feelings based on their exper ience andsavvy

Who under stand the curr ent marketplace and what¶s likely tooccur

Qualitative Methods




12

Qualitative MethodsSubjective or judgmental der ived for ecasts using intuitive or gut feelings

Independent Judgment

Committees

Sales For ce Estimates




13


Committees


Also known as ³Sales For ce Composites´





14


Committees


Also known as ³Sales For ce Composites´

Jur ies of Executive Opinion





15


Advantages

Low cost to develop Executives usually have a solid under standing of the br oad-based

factor s and how they affect sales demand

Pr ovides input f r om the fir m¶s key functional ar eas

Can pr ovide sales for ecasts fair ly quickly




16

They ar e always ³biased´ towar d the user gr oup

They ar e ³not¶ consistently accur ate over time

Some executives may not r eally under stand the fir m¶s sales situation since they ar etoo far r emoved f r om the actual marketplace

Not well suited for fir ms with a lar ge number of pr oducts


Disadvantages




17

Quantitative Methods




18


One Dimensional or Reactive Methods

Time Ser ies Techniques, using only past sales histor y alone

Time Ser ies

Shipments

For

ecas

t




19


Causal

One Dimensional or Reactive Methods

Time Ser ies Techniques, using only past sales histor y alone

Multidimensional or Pr oactive Methods

Causal Techniques, built on a r elationship(s) between past sales andsome other var iable(s)

Time Ser ies

Pr ice

Pr omo

ShipmentsShipments

For

ecas

t

For

ecast




20

Quantitative MethodsObjective mathematically der ived for ecasts.

Times Ser ies Techniques Naive

Simple Moving Aver aging

Exponential Smoothing

Br own¶s Double Exponential Smoothing

Holt's Two Par ameter Exponential Smoothing

Winter ¶s Thr ee Par ameter Exponential Smoothing Decomposition

Multiplicative

Additive

Census X-11

Box-Jenkins




21

Time Ser ies Methods(One Dimensional or Reactive Methods)

Advantages

They ar e well suited to situations wher e sales for ecasts ar e needed for a lar genumber of pr oducts

They work ver y well for pr oducts with fair ly stable sales

They can smooth out small r andom fluctuations

They ar e simple to under stand and use

They can be easily systematized and r equir e little data stor age

Softwar e packages ar e usually accessible, and

They ar e gener ally good at shor t-ter m for ecasting




22

Time Ser ies Methods(One Dimensional or Reactive Methods)

Disadvantages

They r equir e a lar ge amount of histor ical data

They adjust slowly to changes in sales

A gr eat deal of sear ching may be needed to find the weighted(Alpha) value

They usually fall apar t when the for ecast hor izon in long, and

For ecasts can be thr own into gr eat err or because of lar ge

fluctuations in curr ent data




23

Quantitative MethodsObjective mathematically der ived for ecasts.

Causal Techniques

Simple Regr ession

Multiple Regr ession

Econometr ic Modeling

Robust Regr ession




24

When and who invented r egr ession?

The ter m r egr ession was intr oduced by Fr ancis Galton in 1886.

He called it the ³Law of Univer sal Regr ession.´

His f r iend Kar l Pear son confir med the theor y by collecting athousand r ecor ds of heights for childr en of tall and shor t par ents.

Sir Henr y Moor e in 1918 developed the fir st Econometr ic Model.

Things to Remember about Regr ession...




25

Why Haven¶t Causal Methods been Used?

They ar e mor e time-intensive to develop and r equir e a str ongunder standing of statistics

They r equir e lar ger data stor age and ar e less easily systematized,and

They tend to be mor e expensive to build and maintain




26

Why Ar e Causal Methods the wave

of the Futur e?

Enabled by the advent of the PC and Client Ser ver Technology

Available in most softwar e packages

Pr ovide accur ate shor t-, medium-, and long-ter m for ecasts

Ar e capable of suppor ting ³What-if´ analysis




27

Causal Methods(Multidimensional or Pr oactive Methods)

Advantages

They ar e available in most softwar e packages

They ar e inexpensive to r un on computer s

These techniques ar e cover ed in most statistics cour ses so theyhave become incr easingly familiar with manager s

They pr ovide accur ate shor t-, medium-, and long-ter m for ecasts,and

They ar e capable of suppor ting ³What-if´ analysis




28

Causal Methods(Multidimensional or Pr oactive Methods)

Disadvantages

Their for ecasting accur acy depends on a consistent r elationshipbetween independent and dependent var iables

An accur ate estimate of the independent var iable is cr ucial

A lack of under standing by many manager s who view it as a ³black

box´ technique

They ar e mor e time-intensive to develop and r equir e a str ongunder standing of statistics

They r equir e lar ger data stor age and ar e less easily systematized,and

They tend to be mor e expensive to build and maintain




29

Tool Kit Appr oach

Selecting the Appr opr iate Method Based On Por tfolio Management




30

Pr oduct Por tfolio

Stable

Incomplete Complete

Unstable

Data




32

Pr oduct Por tfolio

Incomplete Complete

Unstable

Committees

Sales For ceComposites

IndependentJudgment

Simple MovingAver age

Stable

Data




33

Pr oduct Por tfolio

Incomplete Complete

Unstable

Committees


IndependentJudgment


Census X-11Box-Jenkins

Winter s

Stable

Data




34

Pr oduct Por tfolio

Incomplete Complete

Unstable


Committees


IndependentJudgment



Winter s

Simple Reg

r ession

Stable

Data




35

Pr oduct Por tfolio

Incomplete Complete

Unstable


Committees


IndependentJudgment



Winter s

Simple Reg

r ession

RobustRegr ession

Stable

Data




36

Pr oduct Por tfolio

Incomplete Complete

Unstable


Committees


IndependentJudgment



Winter s

Simple Reg

r ession

RobustRegr ession

BusinessBusinessStr ategyStr ategy

DemandDemand

PullPull

Factor yFactor yPushPush

Stable

Data




37

Pr oduct Por tfolio

Incomplete Complete

Unstable


Committees


IndependentJudgment



Winter s

Simple Reg

r ession

RobustRegr ession

10%

Stable

Data




Complete

Unstable


Committees


IndependentJudgment


Incomplete


Winter s

Simple Reg

r ession

RobustRegr ession

50%

Stable

Pr oduct Por tfolio

Data




Incomplete

Unstable

Complete


Committees


IndependentJudgment



Winter s

Simple Reg

r

ession

RobustRegr ession

35%

Stable

Pr oduct Por tfolio

Data




Incomplete Complete

Unstable


Committees


IndependentJudgment



Winter s

Simple Regr

ession

RobustRegr ession

5%

Stable

Pr oduct Por tfolio

Data




Incomplete Complete

Unstable


Committees


IndependentJudgment


Winter s

Simple Regr

ession

RobustRegr ession

5%

50%

10%

35%


Stable

Pr oduct Por tfolio

Data




Benefits of the For ecast Tool Kit

Appr oach

Better under stand what method(s) to apply to each pr oduct gr oupin your pr oduct por tfolio

Deter mine wher e additional data is r equir ed

How to staff your for ecasting r esour ces

Justifies the r equir ements for a system suppor t tool thatencompasses the complete tool kit of for ecasting methods




Building A Model...

Yi = B0 + B1X1...BnXn + ei




Components of Applied Market Response Modeling

Specification: The model building activity. Involves the client (i.e., Pr oduct Management)

Estimation: Fitting the model to the data.

Includes collecting the data.

Ver ification: Testing the model.

Pr ediction: For ecasting

Four PhasesFour Phases




Thr ee Major By-Pr oductsof Market Response Models

Str uctur al Analysis

Estimation of the impact of such things as pr ice and adver tising on demand asmeasur ed by elasticity's.

Policy Evaluation

The impact of policies that may affect consumer demand, such as pr icing

changes. For ecasting

For ecasting demand of par ticular items in either the shor t-r ange or long-r ange.




46

Model BuildingPr ocess

Fir st, we will identify and assess the facto

r s that ma

ke up themarketing mix (consumption) for a par ticular pr oduct. This is

known as ³Str uctur al Analysis.´

Next, via simulation, begin to deter mine possible alter nativepolicies.

Then, we will pr oduce sales for ecasts for consumer demand.

Finally, tie the outcome to factor y shipments via a second modelto for ecast customer demand (shipments).

This pr ocess of linking causal models together is known as³Multi-Tier ed Causal Analysis´




47

In other Wor ds... Economics 101

RetailMarket(Demand)




48



Factor yShipments(Supply)




49







50







51







52

The Multiple Regr ession Model

Yi = Fo + F1X1 + F2X2... + FnXn + e i

DependentVar iable

Constant Coefficients Explanator yVar iables

StochasticDistur banceTer m




53

The Multiple Regr ession Model

Yi = Fo + F1X1 + F2X2... + FnXn

DependentVar iable

Constant Coefficients Explanator yVar iables

The r egr ession method we will use is called

³Or dinar y Least Squar es.´




54

What to Remember ???

Car l Fr iedr ich Gauss, a Ger man mathematician developed the method of Or dinar y Least Squar es Regr ession.

This method has some ver y attr active statistical pr oper ties that have made itone of the most popular methods of r egr ession analysis.

Or dinar y Least Squar es r egr ession may be a linear modeling appr oach, but

many times it works in situations that you would think it nor mally would not...

Regr ession models ar e r eally called condition models because they modelcurr ent conditions.

In this case curr ent conditions occurr ing in the marketplace ar ound a specificpr oduct line.




55

Phase I.

Specification: The model building activity.

Involves the client (i.e., Pr oduct Management)




56

Pr oduct XRetail Ver sus Shipments

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

J a n

- 9 3

M a r - 9 3

M a y - 9 3

J u l - 9 3

S e p

- 9 3

N o v - 9 3

J a n

- 9 4

M a r - 9 4

M a y - 9 4

J u l - 9 4

S e p

- 9 4

N o v - 9 4

J a n

- 9 5

M a r - 9 5

M a y - 9 5

J u l - 9

5

S e p

- 9 5

N o v - 9 5

J a n

- 9 6

Month/Yr .

units

0

100000

200000

300000

400000

500000

600000

Shipments Retail




57

Phase II.

Estimation: Fitting the model to the data.

Includes collecting the data




58

Or iginal Var iables

M ON TH R eta il S TORE ACVF ACVD ACVDF DP RI C E FS I CABLE GR P B ARTER SP OT P RI C E N P RI C E CAM CP I ME DI A

Ja n-93 360946 84.60 22.51 0.77 0.61 9.70 0 0 8 0 1 10.11 10.22 6547 4.5 584000

Fe b -9 3 337538 80.00 13.00 0.00 0.00 7.00 0 0 0 0 0 10.10 10.10 7174 4.5 1099000

Mar-93 339249 82.51 34.68 0.50 0.09 7.33 0 0 0 0 0 10.10 10.47 7391 4.3 2468000

Apr-93 459376 82.49 33.21 0.11 0.13 11.05 0 0 0 0 0 10.14 10.43 7741 4.5 1395000

May-93 348480 82.43 14.47 0.31 0.00 9.34 0 0 0 0 0 10.08 10.19 6908 4.5 1824000

Jun-93 375431 82.46 29.77 0.39 0.00 12.62 0 0 0 0 0 10.05 10.28 8392 4.2 4670000

Jul-93 388201 83.63 19.54 0.24 0.00 8.76 0 0 0 0 0 10.13 10.26 8476 3.9 1077000

Aug -93 305836 79.79 29.22 0.17 0.04 6.36 0 0 0 0 0 10.11 10.26 7174 3.9 2122000

S e p-9 3 288724 80.43 6.82 0.33 0.00 6.91 33166 0 0 0 0 10.16 10.22 5811 3 .8 4603000

Oc t-93 411043 79.01 29.84 0.80 0.06 6.31 0 0 0 0 0 10.28 10.52 8686 3.9 2967000

No v-93 339806 83.02 35.75 0.53 0.06 6.49 0 0 0 0 0 10.10 10.36 8213 3.8 3122000

D e c-9 3 530741 85.81 38.93 1.52 0.01 10.29 0 0 0 0 0 10.13 10.34 18367 3 .9 3185000

Ja n-94 317279 81.02 23.84 0.75 0.00 11.03 0 0 0 0 0 10.43 10.58 6982 3.6 854000Fe b -9 4 260120 81.23 11.32 1.18 0.00 6.51 0 0 0 0 0 10.51 10.62 5338 3.6 1453000

Mar-94 311943 82.87 32.13 0.88 0.00 6.30 0 0 0 0 0 10.48 10.62 5074 3.6 2404000

Apr-94 381634 83.46 10.48 0.16 0.00 7.31 0 0 0 0 0 10.57 10.68 7354 3.4 1408000

May-94 296083 81.16 29.33 0.10 0.03 7.01 0 0 0 0 0 10.59 10.75 4752 3.3 1516000

Jun-94 307453 81.85 14.69 0.42 0.01 6.50 0 0 0 0 0 10.53 10.66 5245 3.6 3556000

Jul-94 363155 81.98 25.16 0.92 0.00 8.12 0 0 0 0 0 10.61 10.78 7069 4 1341000

Aug -94 300288 79.87 27.55 0.15 0.03 6.90 0 0 0 0 0 10.63 10.77 4365 4.2 1788000

S e p-9 4 286932 80.80 8.63 0.24 0.00 10.36 0 0 0 0 0 10.58 10.71 3260 4.3 2341000

Oc t-94 379779 81.62 31.29 0.81 0.00 8.97 0 87 303 67 4 10.55 10.72 5600 3 .8 2291000

No v-94 313691 80.91 8.89 0.31 0.11 11.60 0 112 231 64 8 10.51 10.59 4310 3 .9 2808000

D e c-9 4 492106 83.42 15.76 0.16 0.17 10.88 0 106 112 64 4 10.50 10.59 10433 3.9 2063000

Ja n-95 280779 77.61 6.61 0.16 0.00 8.34 0 0 0 0 0 10.67 10.74 4478 4.1 6 17000

Fe b -9 5 264012 77.13 12.40 0.14 0.00 7.48 0 0 0 0 0 10.66 10.76 3230 4.2 802000

Mar-95 286491 80.18 22.98 0.16 0.00 9.55 0 0 0 0 0 10.53 10.66 4134 4.2 980000

Apr-95 395456 83.48 19.11 0.15 0.04 9.41 64054 108 275 24 28 10.60 10.70 7 697 4.5 1678000

May-95 349945 80.67 28.86 0.27 0.00 6.19 67992 11 34 0 7 10.61 10.73 7175 4.7 1746000

Jun-95 329236 81.93 15.21 0.00 0.00 9.46 0 0 0 0 0 10.49 10.66 6944 4.5 2017000

Jul-95 356813 84.09 26.11 0.01 0.02 10.93 0 0 0 0 0 10.61 10.73 5212 4.1 1410000

Aug -95 297439 81.61 26.37 0.30 0.02 6.69 0 0 0 0 0 10.65 10.78 6687 3.9 2008000

S e p-9 5 298422 81.87 11.36 0.00 0.00 7.13 0 0 0 0 0 10.71 10.76 4658 3.8 2466000

Oc t-95 368086 83.30 31.70 0.00 0.00 9.65 0 0 0 0 0 10.67 10.82 7841 4.2 2291000

No v-95 321278 82.46 10.64 0.03 0.00 10.79 0 0 0 0 0 10.54 10.65 6907 3.9 2054000

D e c-9 5 501781 84.81 15.01 0.82 0.13 13.23 0 0 0 0 0 10.56 10.63 15543 3 .8 1458000

Ja n-96 306368 80.80 6.43 0.15 0.00 7.72 0 0 0 0 0 10.73 10.80 6076 4.1 6 17000

Fe b -9 6 270453 79.52 9.02 0.66 0.00 5.86 0 0 0 0 0 10.92 10.96 5666 4 8 02000




59

Pr oduct XDemand Model

R2 = .9152 DW = 1.509Adj. R2 = .8880 F-Stat = 33.598 n = 38

Pr od X = Npr ice+Cam +Media [-1] +Adv +Stor e + ACV F + Easter + Xmas + FSI + Constant

Coeff -36246 4.93 .012839 135.55 4819.1 1104.7 67439.0 105380.0 .37309 235550t-Stat -1.85 1.44 3.24 1.70 1.84 2.55 4.42 3.39 1.50 .78

M Elasticity -1.11 .099 .072 .007 1.14 .066 .015 .024 .005 .68Pt Elasticity - .77 .150 .040 n/a .81 .030 n/a .210 n/a n/a

Estimation Phase:Estimation Phase:The model building activities.The model building activities.




60

Summar y of Findings

Marketing Mix Models




61



Gaining stor e distr ibution is the second most effective dr iver of volume.




62




Mer chandising payback with in stor e featur es is above aver age compar ed toother br ands modeled.




63





Adver tising combined with FSI coupons show potential, but it is har d todeter mine whether the spending is sufficient.




64






Pr icing




65






Pr icing

Pr ice is the most significant or effective dr iver of volume.




66






Pr icing

Pr ice is the most significant or effective dr iver of volume.

Acr oss near ly all measur ed channels, the br and shows pr ice elasticity¶s ar eabove the optimal pr ice point.




67

Pr icing Analysis

310000

320000

330000

340000

350000

360000

370000

380000

10.3 10.49 10.67 10.7 10.72Pr ice

Un

it

s

2300000

2350000

24000002450000

2500000

2550000

2600000

Pr ice Units % Chg Fr om$10.49

Revenue Mar gin

$10.30 373781 1.8% $2,541,711 $6.99

$10.49 344905 0% $2,425,126 $6.80

$10.67 337478 -1.7% $2,410,886 $7.17

$10.70 336823 -2.0% $2,419,717 $7.20

$10.72 334205 -2.2% $2,412,960 $7.22

Simulation Phase:Simulation Phase:




68

R2 = .9152 DW = 1.509 DH = 1.2912Adj. R2 = .8880 F-Stat = 33.598 n = 38


Coeff -36246 4.93 .012839 135.55 4819.1 1104.7 67439.0 105380.0 .37309 235550t-Stat -1.85 1.44 3.24 1.70 1.84 2.55 4.42 3.39 1.50 .78


Simulation Phase:Simulation Phase:The model building activities.The model building activities.

4049738 = $10.72 + 70506 + $19527M + 178 + 82% + 15%-32% + 55M + 235550

Pr oduct XDemand Model





69



Coeff -36246 4.93 .012839 135.55 4819.1 1104.7 67439.0 105380.0 .37309 235550t-Stat -1.85 1.44 3.24 1.70 1.84 2.55 4.42 3.39 1.50 .78



4049738 = $10.72 + 70506 + $19527M + 178 + 82% + 15%-32% + 55M + 235550

What If:

Pr oduct X RetailDemand Model

4651328 = $10.52 + 80506 + $40000M + 178 + 90% + 15%-32% + 110M + 235550





70



Coeff -36246 4.93 .012839 135.55 4819.1 1104.7 67439.0 105380.0 .37309 235550t-Stat -1.85 1.44 3.24 1.70 1.84 2.55 4.42 3.39 1.50 .78



4049738 = $10.72 + 70506 + $19527M + 178 + 82% + 15%-32% + 55M + 235550

What If:

4651328 = $10.52 + 80506 + $40000M + 178 + 90% + 15%-32% + 110M + 235550

Pr oduct X RetailDemand Model




71

Net Results

A unit incr ease of 601,590 units...

An additional $6,328,727 to the topline for this par ticular pr oduct...

Total cost $21,000,000 acr oss entir e Pr oduct X family line...

Net r etur n f r om Pr oduct X por tfolio of $26,000,000...




72

Phase III.

Ver ification: Testing the model




73

Now we need topr oject explanator y var iables (or dr iver s)

Two Ways to Pr oject Explanator y Dr iver s

Buy outside infor mation that includes for ecasts for out months

Use a time ser ies method to for ecast them out into

the futur e




74

Pr oduct CAM RetailData: Complete and Stable

(Highly Seasonal)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

F e b - 9 2

A p r - 9 2

J u n - 9 2

A u g - 9

2

O c t - 9 2

D e c - 9

2

F e b - 9 3

A p r - 9 3

J u n - 9 3

A u g - 9

3

O c t - 9 3

D e c - 9

3

F e b - 9 4

A p r - 9 4

J u n - 9 4

A u g - 9

4

O c t - 9 4

D e c - 9

4

F e b - 9 5

Month/Yr .

units

Camer a




75

In this case only Cam r etail demand needs to be pr ojected...

Pr oject Explanator y Var iables




76






77



R2 = .9862 DW = 1.851

Adj. R2 = .9867 F-Stat = 32.84 n = 60

MAPE = 2.8%




78

Evaluation Phase:The for ecasting and tr acking activitiesUsing An Ex-Post For ecast

T1 T2 T3

Backcasting

Ex-Post Simulation or

³Historical Simulation´ Ex-Post ForecastEx-Ante

Forecast

Estimation Period

(Today)

Time, t

Sour ce: Rober t S. Pindyck & Daniel L. Rubinfeld,³Econometr ic Models & Economic For ecasts´

(Forecasting)




79

Pr oduct X Retail

Demand ModelEx-post Sales For ecast

Month/Year Actual For ecast Err or

December 1995 501781 464743 7.3%Januar y 1996 306368 283799 7.4%Febr uar y 1996 270453 265476 1.8%

P d t X




80

Pr oduct XRetail Ver sus Fit (Ex-Post)

0

100000

200000

300000

400000

500000

600000

J a

n - 9 3

M a r - 9 3

M a y

- 9 3

J u l

- 9 3

S e

p - 9 3

N o v

- 9 3

J a

n - 9 4

M a r

- 9 4

M a y

- 9 4

J u l

- 9 4

S e

p - 9 4

N o v

- 9 4

J a

n - 9 5

M a r - 9 5

M a y

- 9 5

J u l

- 9 5

S e

p - 9 5

N o v

- 9 5

J a

n - 9 6

Month/Yr .

units

0

100000

200000

300000

400000

500000

600000

Fit Retail




81

Phase IV.

Pr ediction: For ecasting




82

Sour ces of For ecast Err or

The estimation of the par ameter s in the model ar ewr ong.

The r ight hand side var iables (explanator y var iables)have been pr ojected incorr ectly.

Something changes dur ing the ex-ante for ecastper iods.

Product X




83

Pr oduct XRetail Ver sus Shipments

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

J a n

- 9 3

M a r - 9 3

M a y

- 9 3

J u l

- 9 3

S e p

- 9 3

N o v

- 9 3

J a n

- 9 4

M a r - 9 4

M a y

- 9 4

J u l

- 9 4

S e p

- 9 4

N o v

- 9 4

J a n

- 9 5

M a r

- 9 5

M a y

- 9 5

J u l

- 9 5

S e p

- 9 5

N o v

- 9 5

J a n

- 9 6

Month/Yr .

units

0

100000

200000

300000

400000

500000

600000

Shipments Retail





84

R2 = .9296 DW = 2.066Adj. R2 = .9210 F-Stat = 108.87 n = 38

Pr od X = Retail + Coop + Cashd + Season ality + Constant

Coeff .57071 43861.0 398.79 .31445 -219700.0t-Stat 2.13 3.163 10.31 2.59 -1.47

M Elasticity .3022 .0621 .6371 .3355 -.3369P Elasticity .8914 .1638 1.6993 .3232 n/a

Runs Test: 22 Runs, 22 Positive, 16 Negative

Nor mal Statistic: .8350

S u at o aseS u at o aseThe model building activities.The model building activities.

Pr oduct X ShipmentCustomer Demand Model





85

R2 = .9296 DW = 2.066Adj. R2 = .9210 F-Stat = 108.87 n = 38

Pr od X = Retail + Coop + Cashd + Season ality + Constant

Coeff .57071 43861.0 398.79 .31445 -219700.0t-Stat 2.13 3.163 10.31 2.59 -1.47

M Elasticity .3022 .0621 .6371 .3355 -.3369P Elasticity .8914 .1638 1.6993 .3232 n/a

Runs Test: 22 Runs, 22 Positive, 16 Negative

Nor mal Statistic: .8350

The model building activities.The model building activities.

Pr oduct X ShipmentCustomer Demand Model

Retail incr eased to 4,651,328 units f r om 4,049,738 units, which, in tur n, incr eased shipmentsf r om 7,473,481 units to 8,042,984 units. This adds $3,417,000 to the bottom line.

What If:




86

Pr oduct X Shipment

Customer Demand ModelEx-post Sales For ecast


December 1995 687958 767100 11.5%Januar y 1996 283797 326795 15.2%

Febr uar y 1996 431132 387863 -10.0 %

Product X




87

Pr oduct XShipments Ver sus Fit (Ex-Post)

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

J a n

- 9 3

M a r

- 9 3

M a y

- 9 3

J u l

- 9 3

S e p

- 9 3

N o v

- 9 3

J a n

- 9 4

M a r

- 9 4

M a y

- 9 4

J u l

- 9 4

S e p

- 9 4

N o v

- 9 4

J a n

- 9 5

M a r - 9 5

M a y

- 9 5

J u l

- 9 5

S e p

- 9 5

N o v

- 9 5

J a n

- 9 6

Month/Yr .

units

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

Fit Shipments




89

R-SQUARE = 0.9553 R-SQUARE ADJUSTED = 0.9458

VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY

NAME COEFFICIENT ERROR 19 DF P-VALUE CORR. COEFFICIENT AT MEANS

DS 1.0153 0.4024E-01 25.23 0.000 0.985 0.5713 0.6917

PRICE -96001. 0.1968E+05 -4.878 0.000-0.746 -0.0916 -0.8333

STORE 3655.1 278.8 13.11 0.000 0.949 0.2610 0.5430

ACVA 3118.5 645.4 4.832 0.000 0.743 0.1310 0.0995

CONSTANT 0.10322E+06 0.3649E+05 2.829 0.011 0.544 0.0000 0.5235

DURBIN-WATSON = 1.9233 VON NEUMANN RATIO = 2.0069 RHO = -0.01099RUNS TEST: 8 RUNS, 16 POS, 0 ZERO, 8 NEG NORMAL STATISTIC = -1.7317

DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.11333


Pr oduct Y Retail (Super market Channel)Demand Model

Pr od Y = pr ice + Stor e + ACVA + DSeason[-12] + Constant

Note: Product Y is a Coca-Cola Product in the USA




90

Pr oduct Y Retail

Demand ModelEx-post Sales For ecast


October 1997 464810 412480 11.3%November 1997 296730 296730 0.0%December 1997 184750 206360 - 11.7%




91

Pr od Y = Retail + Constant

Pr oduct Y Bottler ShipmentCustomer Demand Model



VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY

NAME COEFFICIENT ERROR 22 DF P-VALUE CORR. COEFFICIENT AT MEANSRSALES 0.39926 0.4308E-01 9.267 0.000 0.892 0.8205 0.8186

CONSTANT 15148. 0.1212E+05 1.250 0.224 0.258 0.0000 0.1575

DURBIN-WATSON = 1.4837

RUNS TEST: 14 RUNS, 12 POS, 0 ZERO, 12 NEG NORMAL STATISTIC = 0.4174

DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 1.5549

MODIFIED FOR AUTO ORDER=1




92

Pr oduct Y Bottler Shipment

Customer Demand ModelEx-post Sales For ecast


October 1997 188520 200730 - 6.5%November 1997 114960 133620 - 16.2%

December 1997 89209 88911 0.3%




93

Pr od Y = BShipments + Constant

Pr oduct Y TCCC ShipmentBottler Demand Model



VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 30 DF P-VALUE CORR. COEFFICIENT AT MEANS

SEASON3 -0.21269 0.5864E-01 -3.627 0.000-0.552 -0.2167 -0.1933

BSALES 1.1570 0.6460E-01 17.91 0.000 0.956 1.0809 1.1221

CONSTANT 6307.6 5866. 1.075 0.282 0.193 0.0000 0.0713

DURBIN-WATSON = 1.9460

RUNS TEST: 16 RUNS, 14 POS, 0 ZERO, 19 NEG NORMAL STATISTIC = -0.4062

DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 0.89408E-01MODIFIED FOR AUTO ORDER=1 WITH LAGGED DEPVAR




94

Pr oduct Y TCCC Shipment

Bottler Demand ModelEx-post Sales For ecast


October 1997 174690 180390 - 3.3%November 1997 91301 101550 - 11.2%

December 1997 60253 61325 - 1.8%




95

Concer ns/Caveats

Regr ession analysis is a technique that uses changes in data sets to establishstatistical r elationships.

For example, an independent var iable shown not to be significant in ther egr ession equation may still influence the dependent var iable, but ther elationship may not be identified due to a lack of data inter action.

Also, this analysis was done on aggr egated r etail market level which may notnecessar ily r epr esent behavior s at the stor e level. This is a pr oblem that isalways encounter ed when using syndicated market data in r egr essionanalysis.

To pr ecisely evaluate pr omotional effectiveness, stor e level r egr ession modelsor household level logit models must be used.

Forecasting Experience With Market Response




96

For ecasting Exper ience With Market ResponseModels

For ecasts using market r esponse models ar e gener ally super ior to those basedon simple extr apolation techniques.

Market r esponse models pr ovide a useful star ting place for for mulating thefor ecast; identifying factor s for which judgmental decisions can be made; andpr ovide a f r amework to insur e inter nal consistency of the for ecast pr ocess(r ole of identities).

For ecasts with subjective adjustments gener ally ar e mor e accur ate than thoseobtained f r om the ³pur ely´ mechanical application of the r egr ession model (acombination of model building and subjective exper tise).




97

Composite For ecasting

Judgmental




98

What is Composite For ecasting?

Combines for ecasts f r om alter native methods (i.e., Time Ser ies, Causal, and/or Judgment) for a par ticular br and, pr oduct family, pr oduct.

Either by simply aver aging the for ecasts giving each equal weight, or byweighting each for ecast and summing them based on the r esidual err or associated with each method.

The under lying objective is to take advantage of the str engths of each method

to cr eate a single for ecast.

By combining the for ecasts the business analyst¶s objective is to develop thebest for ecast possible.

The composite for ecasts of sever al mathematical and/or judgmental methodshave been pr oven to out per for m the individual for ecasts of any of thosemethods used to gener ate the composite.




99

Simple Aver aging

Example: Simple aver aging of sever al for ecasting methods

CF = FM1 + FM2 + FM3

3

Actual Wi nter's Causal ARIM A Simple Average

Sales H istory M odel M odel M odel Composite Forecast

0 189325 157566 205091 183994

0 145453 143910 151363 146909

0 152675 158359 152666 1545670 238260 215284 258450 237331

0 224234 229538 232486 228753

0 314142 272172 316594 300969




100

Example:Minimum variance weighting minimizes the variance of the forecast errors over

the forecast period.

CF = w1 FM1 + w2 FM2 + w3 FM3

Step 1) Cr eate Ex-Post For ecasts for each method

M onth/Week Actual Wi nter's Causal ARIM A

Period(s) Sales H istor M odel M odel M odel

Ex- Post Ex- Post Ex- Post

Forecast Forecast Forecast

25 123449 103781 112058 124268

26 95435 84243 83997 79842

27 94028 97426 93908 99472

28 161075 144852 136698 183625

29 144031 149053 130834 19527530 196730 215001 194093 248136

31 385962 375566 331835 348688

32 373273 38404 353199 350157

33 417806 402782 344688 360525

34 464806 437483 364587 314270

35 296731 267229 221864 244690

36 184748 208968 168609 164711

Weighted Aver aging




101

Step 2) Run an Or dinar y Least Squar es (OLS) r egr ession model. Using the Actualhistor y for the last 12 per iods as the dependent var iable and the ex-postfor ecasts of the thr ee models as the independent var iables we r estr ict the thr eeindependent var iables to equal 1. This causes the coefficients of the

independent var iables to equal one becoming our weights.

Wher e:

OLS Actual F1Winter + F2Causal + F%6-1% + FCSnstant /Restr ict

Restr ict Winter + Causal + ARIMA = 1

Weighted Aver aging




102

Weighted Aver aging


V ARIANCE OF THE ESTIM ATE-SIGM A**2 = 0.18323E+10

STANDARD ERROR OF THE ESTIM ATE-SIGM A = 42805.

SUMOF SQUARED ERRORS-SSE= 0.16490E+11

MEAN OF DEPENDENTV ARIABLE = 0.24484E+06

LOG OF THE LIKELIHOOD FUNCTION = -143.574

VARIABLE ESTIMATED STAND T-RATIO PART STAND ELASTICIT Y

NAME COEFFICIENT ERROR 9 DF P-VALUE CORR. COEFF AT MEANS

WINTER 0.17581 0.09923 1.772 0.110 0.509 0.1743 0.1511

CAUSAL 0.28493 0.4545 0.6269 0.546 0.205 0.2125 0.2632

ARIMA 0.53926 0.4290 1.257 0.240 0.386 0.3081 0.4030

CONSTANT 36548. 35810 1.021 0.334 0.322 0.0000 0.1493

DURBIN-WATSON = 1.5182 VON NEUM ANN RATIO = 1.6563 RHO = 0.17868

RESIDUALSUM = 19379. RESIDUAL V ARIANCE = 0.18740E+10

SUMOF ABSOLUTE ERRORS= 0.36853E+06

R-SQUAREBETWEEN OBSERVED AND PREDICTED = 0.9431

RUNS TEST: 5 RUNS, 5 POS, 0 ZERO, 7 NEG NORMAL STATISTIC = -1.1451

DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 0.92103

MODIFIED FOR AUTO ORDER=1

W i h d A i




103

Weighted Aver aging

Step 2) The sum of the coefficients of the thr ee models should equal one (e.g., .18+.28+. 54 = 1), and pr opor tioned based on their r esidual err or s accor dingly. Thefinal steps ar e to multiple the coefficients (weights) by their corr espondingor iginal model¶s for ecasts and sum the thr ee for ecasts.

Actual Wi nter's Causal ARIM A Variance Weighted

Sales H istory M odel M odel M odel Com osite Forecast

wt=.18 wt=.28 wt=.54

0 189325 157566 205091 188946

0 145453 143910 151363 148212

0 152675 158359 152666 154262

0 238260 215284 258450 242729

0 224234 229538 232486 230175

0 314142 272172 316594 303714

Cl i Th ht



Closing Thoughts...

Your market, pr oducts, goals, and constr aints shouldbe consider ed when selecting the for ecasting toolsbest for you...

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