APO DP Forecasting

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

Selecting the RightForecasting Forecasting MethodMethod


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Agenda Traditional Sales Forecasting Methods

Current Sales Forecasting Methods and Techniques Being Used Underlying Theory of Forecasting Methods

Sales Forecasting Methodologies

Quantitative vs Qualitative Tool Kit Approach

Build a Model

Components of Applied Market Response Modeling Analyze an Actual Model Using Live Data Introduction to Multi-Tiered Causal Analysis

Composite Forecasting Application


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Most companies seem to use simple techniques that are easy to comprehend and mostly those that involve judgment by company employees.

A method widely used results in forecast goal-setting, this is not really forecasting.

Here companies begin their planning process with a corporate goal to increase sales by some percentage.

This target often comes directly from the chief executive officer. Then everyone backs into their target based on what each business unit manager thinks they can

deliver. Finally, if they don’t meet the target when totaled the CEO either assigns targets to particular

business units or puts a financial plug in place hoping someone will over deliver.

Traditional Sales Forecasting Methods...


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Current Sales Forecasting Methods and Techniques Being Used

More focus on utilizing time series methods to predict baseline sales demand

Primarily using Winter’s Exponential Smoothing Also, some Decomposition/Census X-11 Very little ARIMA/Box-Jenkins

Judgmental techniques still seem to be the dominant method of choice

Sales Force Composites Jury of Executive Opinion Delphi Approach

Multiple Regression is beginning to be utilized

More Universities are teaching Regression Applications Accessing causal data is becoming easier Regression is required to evaluate and predict sales promotions


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Underlying Theory of Forecasting Methods...


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Forecast = Pattern + Randomness



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This simple equation is really saying that when the averagepattern of the underlying data has been identified somedeviation will occur between the forecasting method appliedand the actual occurrence.


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Sales Forecasting Methods...


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Two Types Of Sales Forecasting Methodologies

Qualitative

Also Known as “Judgmental” or Subjective

Quantitative

Also known as “Mathematical” or Objective


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Are also known as Judgmental

Rely on subjective assessments of a person or group of people

Using intuitive or gut feelings based on their experience and savvy

Who understand the current marketplace and what’s likely to occur

Qualitative Methods


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Qualitative MethodsSubjective or judgmental derived forecasts using intuitive or gut feelings

Independent Judgment

Committees

Sales Force Estimates


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Committees


Also known as “Sales Force Composites”



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Committees


Also known as “Sales Force Composites”

Juries of Executive Opinion



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Advantages

Low cost to develop

Executives usually have a solid understanding of the broad-based factors and how they affect sales demand

Provides input from the firm’s key functional areas

Can provide sales forecasts fairly quickly


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They are always “biased” toward the user group

They are “not’ consistently accurate over time

Some executives may not really understand the firm’s sales situation since they are too far removed from the actual marketplace

Not well suited for firms with a large number of products


Disadvantages


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Quantitative Methods


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One Dimensional or Reactive Methods

Time Series Techniques, using only past sales history alone

Time Series

Shipments

Forecast


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Causal

One Dimensional or Reactive Methods

Time Series Techniques, using only past sales history alone

Multidimensional or Proactive Methods

Causal Techniques, built on a relationship(s) between past sales and some other variable(s)

Time Series

Price

PromoShipmentsShipments

Forecast

Forecast


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Quantitative MethodsObjective mathematically derived forecasts.

Times Series Techniques Naive

Simple Moving Averaging

Exponential Smoothing

Brown’s Double Exponential Smoothing Holt's Two Parameter Exponential Smoothing Winter’s Three Parameter Exponential Smoothing

Decomposition

Multiplicative Additive

Census X-11

Box-Jenkins


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Time Series Methods(One Dimensional or Reactive Methods)

Advantages

They are well suited to situations where sales forecasts are needed for a large number of products

They work very well for products with fairly stable sales

They can smooth out small random fluctuations

They are simple to understand and use

They can be easily systematized and require little data storage

Software packages are usually accessible, and

They are generally good at short-term forecasting


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Time Series Methods(One Dimensional or Reactive Methods)

Disadvantages

They require a large amount of historical data

They adjust slowly to changes in sales

A great deal of searching may be needed to find the weighted (Alpha) value

They usually fall apart when the forecast horizon in long, and

Forecasts can be thrown into great error because of large fluctuations in current data


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Quantitative MethodsObjective mathematically derived forecasts.

Causal Techniques

Simple Regression

Multiple Regression

Econometric Modeling

Robust Regression


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When and who invented regression?

The term regression was introduced by Francis Galton in 1886.

He called it the “Law of Universal Regression.”

His friend Karl Pearson confirmed the theory by collecting a thousand records of heights for children of tall and short parents.

Sir Henry Moore in 1918 developed the first Econometric Model.

Things to Remember about Regression...


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Why Haven’t Causal Methods been Used?

They are more time-intensive to develop and require a strong understanding of statistics

They require larger data storage and are less easily systematized, and

They tend to be more expensive to build and maintain


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Why Are Causal Methods the wave of the Future?

Enabled by the advent of the PC and Client Server Technology

Available in most software packages

Provide accurate short-, medium-, and long-term forecasts

Are capable of supporting “What-if” analysis


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Causal Methods(Multidimensional or Proactive Methods)

Advantages

They are available in most software packages

They are inexpensive to run on computers

These techniques are covered in most statistics courses so they have become increasingly familiar with managers

They provide accurate short-, medium-, and long-term forecasts, and

They are capable of supporting “What-if” analysis


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Causal Methods(Multidimensional or Proactive Methods)

Disadvantages

Their forecasting accuracy depends on a consistent relationship between independent and dependent variables

An accurate estimate of the independent variable is crucial

A lack of understanding by many managers who view it as a “black box” technique

They are more time-intensive to develop and require a strong understanding of statistics

They require larger data storage and are less easily systematized, and

They tend to be more expensive to build and maintain


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Tool Kit Approach

Selecting the Appropriate Method Based On Portfolio Management


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Product Portfolio

Stable

Incomplete Complete

Unstable

Data


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Product Portfolio

Incomplete Complete

Unstable

•Committees

•Sales Force Composites

•Independent Judgment

•Simple MovingAverage

Stable

Data


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Product Portfolio

Incomplete Complete

Unstable

•Committees




•Census X-11•Box-Jenkins

•Winters

Stable

Data


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Product Portfolio

Incomplete Complete

Unstable

•Multiple Regression

•Committees





•Winters

•Simple Regression

Stable

Data


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Product Portfolio

Incomplete Complete

Unstable


•Committees





•Winters


•Robust Regression

Stable

Data


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Product Portfolio

Incomplete Complete

Unstable


•Committees





•Winters



BusinessBusinessStrategyStrategy

DemandDemandPullPull

FactoryFactoryPushPush

Stable

Data


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Product Portfolio

Incomplete Complete

Unstable


•Committees





•Winters



10%

Stable

Data


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Complete

Unstable


•Committees




Incomplete


•Winters



50%

Stable

Product Portfolio

Data


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Incomplete

Unstable

Complete


•Committees





•Winters



35%

Stable

Product Portfolio

Data


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Incomplete Complete

Unstable


•Committees





•Winters


•Robust Regression 5%

Stable

Product Portfolio

Data


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Incomplete Complete

Unstable


•Committees




•Winters


•Robust Regression 5%

50%

10%

35%


Stable

Product Portfolio

Data


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Benefits of the Forecast Tool Kit Approach

Better understand what method(s) to apply to each product group in your product portfolio

Determine where additional data is required

How to staff your forecasting resources

Justifies the requirements for a system support tool that encompasses the complete tool kit of forecasting methods


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Building A Model...

Yi = B0 + B1X1...BnXn + ei


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Components ofApplied Market Response Modeling

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

Estimation: Fitting the model to the data.

Includes collecting the data.

Verification: Testing the model.

Prediction: Forecasting

Four PhasesFour Phases


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Three Major By-Productsof Market Response Models

Structural Analysis

Estimation of the impact of such things as price and advertising on demand as measured by elasticity's.

Policy Evaluation

The impact of policies that may affect consumer demand, such as pricing changes.

Forecasting

Forecasting demand of particular items in either the short-range or long-range.


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Model BuildingProcess

First, we will identify and assess the factors that make up the marketing mix (consumption) for a particular product. This is known as “Structural Analysis.”

Next, via simulation, begin to determine possible alternative policies.

Then, we will produce sales forecasts for consumer demand.

Finally, tie the outcome to factory shipments via a second model to forecast customer demand (shipments).

This process of linking causal models together is known as “Multi-Tiered Causal Analysis”


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In other Words... Economics 101

RetailMarket(Demand)


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FactoryShipments(Supply)


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The Multiple Regression Model

Yi = o + 1X1 + 2X2... + nXn + ei

DependentVariable

Constant Coefficients ExplanatoryVariables

StochasticDisturbanceTerm


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The Multiple Regression Model

Yi = o + 1X1 + 2X2... + nXn

DependentVariable

Constant Coefficients ExplanatoryVariables

The regression method we will use is called “Ordinary Least Squares.”


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What to Remember???

Carl Friedrich Gauss, a German mathematician developed the method of Ordinary Least Squares Regression.

This method has some very attractive statistical properties that have made it one of the most popular methods of regression analysis.

Ordinary Least Squares regression may be a linear modeling approach, but many times it works in situations that you would think it normally would not...

Regression models are really called condition models because they model current conditions.

In this case current conditions occurring in the marketplace around a specific product line.


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Phase I.

Specification: The model building activity.

Involves the client (i.e., Product Management)


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Product XRetail Versus Shipments

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Shipments Retail


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Phase II.

Estimation: Fitting the model to the data.

Includes collecting the data


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Original Variables

MONTH Retail STORE ACVF ACVD ACVDF DPRICE FSI CABLE GRP BARTER SPOT PRICE NPRICE CAM CPI MEDIAJa 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 584000Fe b-93 337538 80.00 13.00 0.00 0.00 7.00 0 0 0 0 0 10.10 10.10 7174 4.5 1099000Ma r-93 339249 82.51 34.68 0.50 0.09 7.33 0 0 0 0 0 10.10 10.47 7391 4.3 2468000Apr-93 459376 82.49 33.21 0.11 0.13 11.05 0 0 0 0 0 10.14 10.43 7741 4.5 1395000Ma y-93 348480 82.43 14.47 0.31 0.00 9.34 0 0 0 0 0 10.08 10.19 6908 4.5 1824000Jun-93 375431 82.46 29.77 0.39 0.00 12.62 0 0 0 0 0 10.05 10.28 8392 4.2 4670000Jul-93 388201 83.63 19.54 0.24 0.00 8.76 0 0 0 0 0 10.13 10.26 8476 3.9 1077000Aug -93 305836 79.79 29.22 0.17 0.04 6.36 0 0 0 0 0 10.11 10.26 7174 3.9 2122000S e p -93 288724 80.43 6.82 0.33 0.00 6.91 33166 0 0 0 0 10.16 10.22 5811 3.8 4603000Oc 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 2967000No 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 3122000De c -93 530741 85.81 38.93 1.52 0.01 10.29 0 0 0 0 0 10.13 10.34 18367 3.9 3185000Ja 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-94 260120 81.23 11.32 1.18 0.00 6.51 0 0 0 0 0 10.51 10.62 5338 3.6 1453000Ma r-94 311943 82.87 32.13 0.88 0.00 6.30 0 0 0 0 0 10.48 10.62 5074 3.6 2404000Apr-94 381634 83.46 10.48 0.16 0.00 7.31 0 0 0 0 0 10.57 10.68 7354 3.4 1408000Ma y-94 296083 81.16 29.33 0.10 0.03 7.01 0 0 0 0 0 10.59 10.75 4752 3.3 1516000Jun-94 307453 81.85 14.69 0.42 0.01 6.50 0 0 0 0 0 10.53 10.66 5245 3.6 3556000Jul-94 363155 81.98 25.16 0.92 0.00 8.12 0 0 0 0 0 10.61 10.78 7069 4 1341000Aug -94 300288 79.87 27.55 0.15 0.03 6.90 0 0 0 0 0 10.63 10.77 4365 4.2 1788000S e p -94 286932 80.80 8.63 0.24 0.00 10.36 0 0 0 0 0 10.58 10.71 3260 4.3 2341000Oc 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 2291000No 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 2808000De c -94 492106 83.42 15.76 0.16 0.17 10.88 0 106 112 64 4 10.50 10.59 10433 3.9 2063000Ja 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 617000Fe b-95 264012 77.13 12.40 0.14 0.00 7.48 0 0 0 0 0 10.66 10.76 3230 4.2 802000Ma r-95 286491 80.18 22.98 0.16 0.00 9.55 0 0 0 0 0 10.53 10.66 4134 4.2 980000Apr-95 395456 83.48 19.11 0.15 0.04 9.41 64054 108 275 24 28 10.60 10.70 7697 4.5 1678000Ma y-95 349945 80.67 28.86 0.27 0.00 6.19 67992 11 34 0 7 10.61 10.73 7175 4.7 1746000Jun-95 329236 81.93 15.21 0.00 0.00 9.46 0 0 0 0 0 10.49 10.66 6944 4.5 2017000Jul-95 356813 84.09 26.11 0.01 0.02 10.93 0 0 0 0 0 10.61 10.73 5212 4.1 1410000Aug -95 297439 81.61 26.37 0.30 0.02 6.69 0 0 0 0 0 10.65 10.78 6687 3.9 2008000S e p -95 298422 81.87 11.36 0.00 0.00 7.13 0 0 0 0 0 10.71 10.76 4658 3.8 2466000Oc 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 2291000No 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 2054000De c -95 501781 84.81 15.01 0.82 0.13 13.23 0 0 0 0 0 10.56 10.63 15543 3.8 1458000Ja 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 617000Fe b-96 270453 79.52 9.02 0.66 0.00 5.86 0 0 0 0 0 10.92 10.96 5666 4 802000


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Product X Demand Model

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

Prod X = Nprice+Cam +Media [-1] +Adv +Store + ACV F + Easter + Xmas + FSI + Constant

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


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Summary of Findings

Marketing Mix Models


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Summary of Findings


Gaining store distribution is the second most effective driver of volume.


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Summary of Findings


Gaining store distribution is the second most effective driver of volume. Merchandising payback with in store features is above average compared to

other brands modeled.


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Summary of Findings



other brands modeled. Advertising combined with FSI coupons show potential, but it is hard to

determine whether the spending is sufficient.


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Summary of Findings





Pricing


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Summary of Findings





Pricing

Price is the most significant or effective driver of volume.


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Summary of Findings





Pricing

Price is the most significant or effective driver of volume. Across nearly all measured channels, the brand shows price elasticity’s are

above the optimal price point.


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Pricing Analysis

310000

320000

330000

340000

350000

360000

370000

380000

10.3 10.49 10.67 10.7 10.72

Price

Units

2300000

2350000

2400000

2450000

2500000

2550000

2600000

Revenue

Price Units % Chg From $10.49

Revenue Margin

$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


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



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

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

Product X Demand Model


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

What If:

Product X Retail Demand Model

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


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

What If:

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

Product X Retail Demand Model


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Net Results

A unit increase of 601,590 units...

An additional $6,328,727 to the topline for this particular product...

Total cost $21,000,000 across entire Product X family line...

Net return from Product X portfolio of $26,000,000...


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Phase III.

Verification: Testing the model


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Now we need toproject explanatory variables (or drivers)

Two Ways to Project Explanatory Drivers

Buy outside information that includes forecasts for out months

Use a time series method to forecast them out into the future


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Product CAM RetailData: Complete and Stable

(Highly Seasonal)

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units

Camera


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In this case only Cam retail demand needs to be projected...

Project Explanatory Variables


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R2 = .9862 DW = 1.851

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

MAPE = 2.8%


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Evaluation Phase:The forecasting and tracking activitiesUsing An Ex-Post Forecast

T1 T2 T3

BackcastingEx-Post Simulation or“Historical Simulation” Ex-Post Forecast

Ex-AnteForecast

Estimation Period

(Today)

Time, t

Source: Robert S. Pindyck & Daniel L. Rubinfeld, “Econometric Models & Economic Forecasts”

(Forecasting)


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Product X RetailDemand ModelEx-post Sales Forecast

Month/Year Actual Forecast Error

December 1995 501781 464743 7.3%January 1996 306368 283799 7.4%February 1996 270453 265476 1.8%


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Product X Retail Versus Fit (Ex-Post)

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Fit Retail


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Phase IV.

Prediction: Forecasting


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Sources of Forecast Error

The estimation of the parameters in the model are wrong.

The right hand side variables (explanatory variables) have been projected incorrectly.

Something changes during the ex-ante forecast periods.


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Product X Retail Versus Shipments

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Shipments Retail


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

Prod X = Retail + Coop + Cashd + Season ality + Constant

Coeff .57071 43861.0 398.79 .31445 -219700.0 t-Stat 2.13 3.163 10.31 2.59 -1.47M Elasticity .3022 .0621 .6371 .3355 -.3369P Elasticity .8914 .1638 1.6993 .3232 n/a

Runs Test: 22 Runs, 22 Positive, 16 NegativeNormal Statistic: .8350


Product X ShipmentCustomer Demand Model


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

Prod X = Retail + Coop + Cashd + Season ality + Constant

Coeff .57071 43861.0 398.79 .31445 -219700.0 t-Stat 2.13 3.163 10.31 2.59 -1.47M Elasticity .3022 .0621 .6371 .3355 -.3369P Elasticity .8914 .1638 1.6993 .3232 n/a

Runs Test: 22 Runs, 22 Positive, 16 NegativeNormal Statistic: .8350


Product X ShipmentCustomer Demand Model

Retail increased to 4,651,328 units from 4,049,738 units, which, in turn, increased shipmentsfrom 7,473,481 units to 8,042,984 units. This adds $3,417,000 to the bottom line.

What If:


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Product X ShipmentCustomer Demand ModelEx-post Sales Forecast


December 1995 687958 767100 11.5%January 1996 283797 326795 15.2%February 1996 431132 387863 -10.0 %


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Product X Shipments Versus Fit (Ex-Post)

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Fit Shipments


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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 = -0.01099 RUNS TEST: 8 RUNS, 16 POS, 0 ZERO, 8 NEG NORMAL STATISTIC = -1.7317 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.11333


Product Y Retail (Supermarket Channel)Demand Model

Prod Y = price + Store + ACVA + DSeason[-12] + Constant

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


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Product Y RetailDemand ModelEx-post Sales Forecast


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


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Prod Y = Retail + Constant

Product Y Bottler ShipmentCustomer Demand Model


R-SQUARE = 0.9410 R-SQUARE ADJUSTED = 0.9383 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITYNAME COEFFICIENT ERROR 22 DF P-VALUE CORR. COEFFICIENT AT MEANSRSALES 0.39926 0.4308E-01 9.267 0.000 0.892 0.8205 0.8186CONSTANT 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 = 0.4174DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 1.5549MODIFIED FOR AUTO ORDER=1


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Product Y Bottler ShipmentCustomer Demand ModelEx-post Sales Forecast


October 1997 188520 200730 - 6.5%November 1997 114960 133620 - 16.2%December 1997 89209 88911 0.3%


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Prod Y = BShipments + Constant

Product Y TCCC ShipmentBottler Demand Model


R-SQUARE = 0.9513 R-SQUARE ADJUSTED = 0.9480 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITYNAME COEFFICIENT ERROR 30 DF P-VALUE CORR. COEFFICIENT AT MEANSSEASON3 -0.21269 0.5864E-01 -3.627 0.000-0.552 -0.2167 -0.1933BSALES 1.1570 0.6460E-01 17.91 0.000 0.956 1.0809 1.1221CONSTANT 6307.6 5866. 1.075 0.282 0.193 0.0000 0.0713

DURBIN-WATSON = 1.9460RUNS TEST: 16 RUNS, 14 POS, 0 ZERO, 19 NEG NORMAL STATISTIC = -0.4062DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 0.89408E-01MODIFIED FOR AUTO ORDER=1 WITH LAGGED DEPVAR


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Product Y TCCC ShipmentBottler Demand ModelEx-post Sales Forecast


October 1997 174690 180390 - 3.3%November 1997 91301 101550 - 11.2%December 1997 60253 61325 - 1.8%


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Concerns/Caveats

Regression analysis is a technique that uses changes in data sets to establish statistical relationships.

For example, an independent variable shown not to be significant in the regression equation may still influence the dependent variable, but the relationship may not be identified due to a lack of data interaction.

Also, this analysis was done on aggregated retail market level which may not necessarily represent behaviors at the store level. This is a problem that is always encountered when using syndicated market data in regression analysis.

To precisely evaluate promotional effectiveness, store level regression models or household level logit models must be used.


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Forecasting Experience With Market Response Models

Forecasts using market response models are generally superior to those based on simple extrapolation techniques.

Market response models provide a useful starting place for formulating the forecast; identifying factors for which judgmental decisions can be made; and provide a framework to insure internal consistency of the forecast process (role of identities).

Forecasts with subjective adjustments generally are more accurate than those obtained from the “purely” mechanical application of the regression model (a combination of model building and subjective expertise).


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Composite Forecasting

Judgmental


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What is Composite Forecasting?

Combines forecasts from alternative methods (i.e., Time Series, Causal, and/or Judgment) for a particular brand, product family, product.

Either by simply averaging the forecasts giving each equal weight, or by weighting each forecast and summing them based on the residual error associated with each method.

The underlying objective is to take advantage of the strengths of each method to create a single forecast.

By combining the forecasts the business analyst’s objective is to develop the best forecast possible.

The composite forecasts of several mathematical and/or judgmental methods have been proven to out perform the individual forecasts of any of those methods used to generate the composite.


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Simple Averaging

Example: Simple averaging of several forecasting methods

CF = FM1 + FM2 + FM3

3

Actual Winter's Causal ARIMA Simple AverageSales History Model Model Model Composite Forecast0 189325 157566 205091 1839940 145453 143910 151363 1469090 152675 158359 152666 1545670 238260 215284 258450 2373310 224234 229538 232486 2287530 314142 272172 316594 300969


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

CF = w1 FM1 + w2 FM2 + w3 FM3

Step 1) Create Ex-Post Forecasts for each method

Month/Week Actual Winter's Causal ARIMAPeriod(s) Sales History Model Model Model

Ex-Post Ex-Post Ex-PostForecast Forecast Forecast

25 123449 103781 112058 12426826 95435 84243 83997 79842

27 94028 97426 93908 9947228 161075 144852 136698 18362529 144031 149053 130834 19527530 196730 215001 194093 24813631 385962 375566 331835 34868832 373273 38404 353199 35015733 417806 402782 344688 36052534 464806 437483 364587 31427035 296731 267229 221864 24469036 184748 208968 168609 164711

Weighted Averaging


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Step 2) Run an Ordinary Least Squares (OLS) regression model. Using the Actual history for the last 12 periods as the dependent variable and the ex-post forecasts of the three models as the independent variables we

restrict the three independent variables to equal 1. This causes the coefficients of the independent variables to equal one becoming our weights.

Where:

OLS Actual 1Winter + 2Causal + + Cnstant /Restrict

Restrict Winter + Causal + ARIMA = 1

Weighted Averaging


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Weighted Averaging

R-SQUARE = 0.9177 R-SQUARE ADJUSTED = 0.8994

VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.18323E+10

STANDARD ERROR OF THE ESTIMATE-SIGMA = 42805.

SUM OF SQUARED ERRORS-SSE= 0.16490E+11

MEAN OF DEPENDENT VARIABLE = 0.24484E+06

LOG OF THE LIKELIHOOD FUNCTION = -143.574

VARIABLE ESTIMATED STAND T-RATIO PART STAND ELASTICITY

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 NEUMANN RATIO = 1.6563 RHO = 0.17868

RESIDUAL SUM = 19379. RESIDUAL VARIANCE = 0.18740E+10

SUM OF ABSOLUTE ERRORS= 0.36853E+06

R-SQUARE BETWEEN 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


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Weighted Averaging

Step 2) The sum of the coefficients of the three models should equal one (e.g., .18+. 28+. 54 = 1), and proportioned based on their residual errors accordingly. The final steps are to multiple the coefficients (weights) by their corresponding original model’s forecasts and sum the three forecasts.

Actual Winter's Causal ARIMA Variance WeightedSales History Model Model Model Composite Forecast

wt=.18 wt=.28 wt=.540 189325 157566 205091 1889460 145453 143910 151363 1482120 152675 158359 152666 1542620 238260 215284 258450 2427290 224234 229538 232486 2301750 314142 272172 316594 303714


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Closing Thoughts...

Your market, products, goals, and constraints should be considered when selecting the forecasting tools best for you...

APO DP Forecasting

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