demand estimation and forecasting

Chapter 5

Demand Estimation and

Forecasting

Copyright ©2014 Pearson Education, Inc. All rights reserved. 5-2

Chapter Outline

• Regression analysis• Limitation of regression analysis• The importance of business forecasting• Prerequisites of a good forecast• Forecasting techniques


Learning Objectives

• Understand the importance of forecasting in business

• Know how to specify and interpret a regression model

• Describe the major forecasting techniques used in business and their limitations

• Explain basic smoothing methods of forecasting, such as the moving average and exponential smoothing


Data Collection

• Statistical analyses are only as good as the accuracy and appropriateness of the sample of information that is used.

• Several sources of data for business analysis:– buy from data providers (e.g. ACNielsen, IRI)– perform a consumer survey– focus groups– technology: point-of-sale data sources


Regression Analysis

• Regression analysis: a procedure commonly used by economists to estimate consumer demand with available data

Two types of regression:– cross-sectional: analyze several variables for a

single period of time– time series data: analyze a single variable over

multiple periods of time


Regression Analysis

• Regression equation: linear, additive

eg: Y = a + b1X1 + b2X2 + b3X3 + b4X4

Y: dependent variablea: constant value, y-interceptXn: independent variables, used to explain Y

bn: regression coefficients (measure impact of independent variables)


Regression Analysis

• Interpreting the regression results: Coefficients:– negative coefficient shows that as the

independent variable (Xn) changes, the variable (Y) changes in the opposite direction

– positive coefficient shows that as the independent variable (Xn) changes, the dependent variable (Y) changes in the same direction

– The regression coefficients are used to compute the elasticity for each variable


Regression Analysis

• Statistical evaluation of regression results:

– t-test: test of statistical significance of each estimated coefficient (whether the coefficient is significantly different from zero)

b = estimated coefficient Seb = standard error of estimated

coefficient

b̂SE

b̂ t


Regression Analysis

• Statistical evaluation of regression results:

– ‘rule of 2’: if absolute value of t is greater than 2, estimated coefficient is significant at the 5% level (for large samples-for small samples, need to use a t table)

– if coefficient passes t-test, the variable has a significant impact on demand


Regression Analysis

• Statistical evaluation of regression results

– R2 (coefficient of determination): percentage of variation in the variable (Y) accounted for by variation in all explanatory variables (Xn)

R2 value ranges from 0.0 to 1.0The closer to 1.0, the greater the explanatory power of the regression.


Regression Analysis

• Statistical evaluation of regression results

– F-test: measures statistical significance of the entire regression as a whole (not each coefficient)


Regression Analysis

• Steps for analyzing regression results

– check coefficient signs and magnitudes

– compute elasticity coefficient

– determine statistical significance


Regression Analysis

• Textbook example: Management lessons from estimating demand for pizza– demand for pizza affected by

1. price of pizza2. price of complement (soda)

– managers can expect price decreases to lead to lower revenue

– tuition and location are not significant


Regression Analysis

• Challenges– Identification– Multicollinearity– Autocorrelation


Regression Analysis

• Challenge 1: Identification problem: – The estimation of demand may produce biased

results due to simultaneous shifting of supply and demand curves.

– Solution: use of advanced correction techniques, such as two-stage least squares and indirect least squares may compensate for the bias


Regression Analysis

• Challenge 2: Multicollinearity problem– Two or more independent variables are highly

correlated, thus it is difficult to separate the effect each has on the dependent variable.

– Solution: a standard remedy is to drop one of the closely related independent variables from the regression


Regression Analysis

• Challenge 3: Autocorrelation problem– Also known as serial correlation, occurs when the

dependent variable relates to the Y variable according to a certain pattern

– Note: possible causes include omitted variables, or non-linearity; Durbin-Watson statistic is used to identify autocorrelation

– Solution: to correct autocorrelation consider transforming the data into a different order of magnitude or introducing leading or lagging data


Forecasting

• “Forecasting is very difficult, especially into the future.”

• Common subjects of business forecasts:– gross domestic product (GDP)– components of GDP

• examples: consumption expenditure, producer durable equipment expenditure, residential construction

– industry forecasts• example: sales of products across an industry

– sales of a specific product


Forecasting

• A good forecast should:– be consistent with other parts of the business– be based on knowledge of the relevant past– consider the economic and political environment

as well as changes– be timely


Forecasting Techniques

• Factors in choosing the right forecasting technique:– item to be forecast– interaction of the situation with the forecasting

methodology--the value and costs– amount of historical data available– time allowed to prepare forecast



• Six forecasting techniques– expert opinion– opinion polls and market research– surveys of spending plans– economic indicators– projections– econometric models



• Approaches to forecasting

– qualitative forecasting is based on judgments expressed by individuals or group

– quantitative forecasting utilizes significant amounts of data and equations



• Approaches to quantitative forecasting:

– naïve forecasting projects past data without explaining future trends

– causal (or explanatory) forecasting attempts to explain the functional relationships between the dependent variable and the independent variables



• Expert opinion techniques

– Jury of executive opinion: forecasts generated by a group of corporate executives assembled together



• Expert opinion techniques

– The Delphi method: a form of expert opinion forecasting that uses a series of questions and answers to obtain a consensus forecast, where experts do not meet



• Opinion polls: sample populations are surveyed to determine consumption trends

– may identify changes in trends– choice of sample is important– questions must be simple and clear



• Market research: is closely related to opinion polling and will indicate not only why the consumer is (or is not) buying, but also

– who the consumer is– how he or she is using the product– characteristics the consumer thinks are most

important in the purchasing decision



• Surveys of spending plans: yields information about ‘macro-type’ data relating to the economy, especially:

– consumer intentions • examples: Survey of Consumers (University of

Michigan), Consumer Confidence Survey (Conference Board)

– inventories and sales expectations



• Economic indicators: a barometric method of forecasting designed to alert business to changes in conditions

– leading, coincident, and lagging indicators

– composite index: one indicator alone may not be very reliable, but a mix of leading indicators may be effective



• Leading indicators predict future economic activity

– average hours, manufacturing– initial claims for unemployment insurance– manufacturers’ new orders for consumer goods

and materials– vendor performance, slower deliveries diffusion

index– manufacturers’ new orders, nondefense capital

goods



• Additional leading indicators to predict future economic activity

– building permits, new private housing units– stock prices, 500 common stocks– money supply, M2– interest rate spread, 10-year Treasury bonds

minus federal funds– index of consumer expectations



• Coincident indicators identify trends in current economic activity

– employees on nonagricultural payrolls– personal income less transfer payments– industrial production– manufacturing and trade sales



• Lagging indicators confirm swings in past economic activity

– average duration of unemployment, weeks– ratio, manufacturing and trade inventories to

sales– change in labor cost per unit of output,

manufacturing (%)



• Additional lagging indicators confirm swings in past economic activity

– average prime rate charged by banks– commercial and industrial loans outstanding– ratio, consumer installment credit outstanding to

personal income– change in consumer price index for services



• Economic indicators: drawbacks

– leading indicator index has forecast a recession when none ensued

– a change in the index does not indicate the precise size of the decline or increase

– the data are subject to revision in the ensuing months



• Trend projections: a form of naïve forecasting that projects trends from past data without taking into consideration reasons for the change

– compound growth rate– visual time series projections– least squares time series projection



• Compound growth rate: forecasting by projecting the average growth rate of the past into the future

– provides a relatively simple and timely forecast– appropriate when the variable to be predicted

increases at a constant percentage



• General compound growth rate formula:

E/B = (1+i)n

E = final value n = years in the series B = beginning value i = constant growth rate



• Visual time series projections: plotting observations on a graph and viewing the shape of the data and any trends



• An Example in Which the Constant Compound Growth Rate Approach Would Be Misleading



• Time series analysis: a naïve method of forecasting from past data by using least squares statistical methods to identify trends, cycles, seasonality, and irregular movements



• Time series analysis:

– easy to calculate– does not require much judgment or analytical

skill– describes the best possible fit for past data– usually reasonably reliable in the short run



• Time series data can be represented as:

Yt = f(Tt, Ct, St, Rt)

Yt = actual value of the data at time t

Tt = trend component at t

Ct = cyclical component at t

St = seasonal component at t

Rt = random component at t



• Time series components: seasonality

– need to identify and remove seasonal factors, using moving averages to isolate those factors

– remove seasonality by dividing data by seasonal factor



• Time series components: trend

– to remove trend line, use least squares method– possible best-fit line styles:

straight line: Y = a + b(t) exponential line: Y = abt

quadratic line: Y = a + b(t) + c(t)2

– choose one with best R2



• Time series components: cyclical, random

– isolate cyclical components by smoothing with a moving average

– random factors cannot be predicted and should be ignored



• Smoothing techniques

– Moving average• The larger the number of observations in the average,

the greater the smoothing effect.

– Exponential smoothing• Allows for the decreasing importance of information in

the more distant past.



• Moving average: average of actual past results used to forecast one period ahead

Et+1 = (Xt + Xt-1 + … + Xt-N+1)/N

Et+1 = forecast for next period

Xt, Xt-1 = actual values at their respective times

N = number of observations included in average



• Exponential smoothing: allows for decreasing importance of information in the more distant past, through geometric progression

Et+1 = w·Xt + (1-w) · Et

w = weight assigned to an actual observation at period t



• Econometric models: causal or explanatory models of forecasting– regression analysis– multiple equation systems

• endogenous variables: dependent variables that may influence other dependent variables

• exogenous variables: from outside the system, truly independent variables



• Illustration of a model of the relationship between the domestic currency and a foreign currency:

Et = a + bIt + cRt + dGt

– where E = Exchange rate of a foreign currency in terms of the domestic currency

– I = Domestic inflation rate minus foreign inflation rate– R = Domestic nominal interest rate minus foreign nominal

interest rate– G = Domestic growth rate of GDP minus the growth rate of

foreign GDP– t = Time period– a, b, c, d Regression coefficients


Summary

• Regression analysis is a primary tool used by businesses to understand demand.

• Reliable input data and proper estimation and evaluation are needed.

• Forecasting is an important activity in many organizations. In business, forecasting is a necessity.

• This chapter summarized and discussed six of the major forecasting techniques used by businesses.

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