Kalman Filter Estimation of New Product Diffusion Models

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Marketing Association is collaborating with JSTOR to digitize, preserve and extend access toThe authors introduce a new estimation procedure, Augmented Kalman Filter with Continuous State and Discrete Observations (AKF(C-D)), for estimating diffusion models. This method is directly applicable to differential diffusion models without imposing constraints on the model structure or the nature of the unknown parameters. It provides a systematic way to incorporate prior knowledge about the likely values of unknown parameters and updates the estimates when new data become available. The authors compare AKF(C-D) empirically with five other estimation procedures, demonstrating AKF(C-D)'s superior prediction performance. As an extension to the basic AKF(C-D) approach, they also develop a parallel-filters procedure for estimating diffusion models when there is uncertainty about diffusion model structure or prior distributions of the unknown parameters. KalmanFilter Estimation o f New Product Diffusion Models The desire to forecast the diffusion of new products has inspired a large body of research during the past two decades. The accurate prediction of new product diffusions is critical in designing marketing strategies for new product planning and management. Before predicting sales, diffusion model specifications must be determined and parameters must be estimated. A variety of estimation methods for estimating diffusion models have been proposed. (For a review of the literature on these estimation techniques, see Mahajan, Muller, and Bass 1990.) In their article, Mahajan, Muller, and Bass (1990) classify diffusion model estimation procedures into two groups: time-invariant estimation procedures and timevarying estimation procedures. Time-invariant estimation procedures include the conventional estimation methods such as ordinary least square (OLS) (Bass 1969), maximum likelihood estimation (MLE) (Schmittlein and Mahajan 1982), and nonlinear least squares (NLS) (Srinivasan and Mason 1986). for their helpful suggestions. They also are thankful to JMR editor Vijay Mahajan and three anonymous reviewers for their insightful and constructive comments.(2) x(t)= [p + q n(t -1) i[m n(t -1)] = oi + a2n(t -1) + oa3n2(t -I), t = 1, 2,.... where x(t) is the number of new adopters in the tth interval, and 378 This content downloaded from 150.135.239.97 on Thu,

Optimal Advertising and Promotion Budgets in Dynamic Markets with Brand Equity as a Mediating Variable

“…In order to obtain estimates of this unobserved brand equity for each period, we use the Kalman filter algorithm, which has been used extensively in control engineering and has been recently applied in the marketing literature (for example, Xie, Sirbu, and Wang 1997;Putsis 1998;Naik, Mantrala, and Sawyer 1998;Akcura, Gonul, and Petrova 2004). The Kalman filter is a recursive algorithm that is used to obtain efficient estimates of an unobserved state variable (which happens to be brand equity in our case) in each period based on the information observed in that period.…”

Do Vegetarian Marketing Campaigns Promote a Vegan Diet?

“…Xie et al (1997) have previously used the extended Kalman filter in diffusion estimation for direct parameter estimation and Naik (2008) have used it to track an endogeneously determined variable in a study of brand awareness in dynamic oligopolies. Our approach is to use the filter as a means of state tracking in conjunction with classical parameter estimation.…”

“…The continuous time and discrete observation extended Kalman filter has been previously used by Xie et al (1997), who use filter projection for simultaneous Bayesian updating of parameter estimates and sales, and Naik et al (2008) who use it to determine the behaviour of endogenous consumer awareness in a dynamic oligopoly. In contrast, our approach takes the parameters outside of the state variable, making them amenable to classical estimation and limiting the impact of prior beliefs on their assessment.…”

Variable Marginal Propensities to Pirate and the Diffusion of Computer Software

“…We allow for cross-sectional relations between legal and pirate diffusion, and present parameter standard deviations unlike prior work. We use the continuous time, discrete observation extended Kalman filter to avoid time interval bias, in common with Xie et al (1997). However, whereas they use the filter projection as a Bayesian updating procedure for parameter estimates and sales simultaneously, we leave the parameters outside the state variable, and so make them available for classical estimation.…”