Adaptive Smoothing using Evolutionary Spectra

The importance of adaptive and exponentially smoothed forecasting has led to the development of several schemes using the tracking signal or the smoothed autocorrelation function for changing the value of the smoothing coefficient. An alternative scheme, using evolutionary spectra is proposed. The smoothing constant is determined as a function of the maximum change in the various frequency components of successive spectra. The location and magnitude of this maximum change also indicates the type of disturbance in the underlying stochastic process generating the series. Simulation experiments indicate that the use of spectra in this evolutionary fashion produces forecasts that are generally more stable as well as more sensitive to genuine changes than schemes based on the tracking signal.

Stochastic Models of a Price Promotion

Stochastic models of a commonly used consumer marketing tool--a price off or price promotion--are developed. Two cases are considered: first, when the duration of the promotion is unknown to customers, and second, when it is known. The optimal duration is derived in both cases as a function of the probability of purchasers of competitive brands switching to the promoted brand, the increased quantity purchased due to the "bargain" and the possible increase in the consumption rate as a consequence. A numerical illustration and a discussion of promotion desirability at different times is presented. Finally, a procedure for estimating model parameters and testing model assumptions is discussed.

A System of Promotional Models

A system of promotional-effect models developed from certain behavioral assumptions about consumer buying habits is described. The same basic model structure is shown to be applicable to several types of gasoline marketing promotions and to various nongasoline promotions as well. Parameter estimation procedures and methods for calculating the effect of simultaneous promotions are discussed. The models were developed to be used with a computerized MIS for market planning and sales forecasting and are validated using actual sales data. Included are insights into the customer buying process that were revealed during the parameter estimation and updating procedures.

Forecasting with a Repeat Purchase Diffusion Model

A methodology for forecasting the sales of an ethical drug as a function of marketing effort before any sales data are available and for updating the forecast with a few periods of sales data is presented. Physicians' perceptions of the drug on a number of attributes, e.g. effectiveness, range of ailments for which appropriate, frequency of prescriptions, are used to estimate the parameters of a model originally proposed by Lilien, Rao and Kalish (Lilien, G. L., A. G. Rao, S. Kalish. 1981. Bayesian estimation and control of detailing effort in a repeat purchase diffusion environment. Management Sci. 27(May) 493--506.). This model conceptualizes the drug adoption process as a repeat purchase diffusion model; sales are expressed as a function of a drug's own and competitive marketing efforts and of word of mouth. The model is first validated in this paper via predictive testing on 19 drugs prescribed by three types of physicians. The forecasting methodology is illustrated using physicians' perceptions on these drugs. Forecasts obtained without any sales data, and updated forecasts using seven periods of sales data are presented, and are encouraging.marketing, buyer behavior, new products, forecasting applications

Reply to Wilfried R. Vanhonacker

No abstract available.

New Models from Old: Forecasting Product Adoption by Hierarchical Bayes Procedures

A method for obtaining early forecasts for the sales of new durable products based on Hierarchical Bayes procedures is presented. The Bass model is implemented within this framework by using a nonlinear regression approach. The linear regression model has been shown to have numerous shortcomings. Two stages of prior distributions use sales data from a variety of dissimilar new products. The first prior distribution describes the variation among the parameters of the products, and the second prior distribution expresses the uncertainty about the hyperparameters of the first prior. Before observing sales data for a new product launch, the forecasts are the expectation of the first stage prior distribution. As sales data become available, the forecasts adapt to the unique features of the product. Early forecasting and the adaptive capability are the two major payoffs from using Hierarchical Bayes procedures. This contrasts with other estimation approaches which either use a linear model or provide reasonable forecasts only after the inflection point of the time series of the sales. The paper also indicates how the Hierarchical Bayes procedure can be extended to include exogenous variables.new product diffusion, Bayes methods, forecasting