The 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.
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References
1.
AthansMichael (1974), “The Importance of Kalman Filtering Methods For Economic Systems,”Annals of Economic and Social Measurement, 3(1), 49–64.
2.
BassFrank M. (1969), “A New Product Growth Model for Consumer Durable,”Management Science, 15(January), 215–27.
3.
BretschneiderStuart I., and MahajanVijay (1980), “Adaptive Technological Substitution Models,”Technological Forecasting and Social Change, 18(October), 129–39.
4.
CarboneRobert, and LonginiRichard L. (1977), “A Feedback Model for Automated Real Estate Assessment,”Management Science, 24, 241–48.
5.
ChenGuangrong, and ChuiCharles K. (1991), “A Modified Adaptive Kalman Filter for Real-Time Applications,”IEEE Transactions on Aerospace and Electronic System, 27(January), 149–53.
6.
DhebarAnirudh, and OrenShmuel S. (1985), “Optimal Dynamic Pricing for Expanding Networks,”Marketing Science, 4(Fall), 36–51.
7.
DuncanGeorge, GorrWilpen L., and SzczypulaJanusz (1993), “Baysian Forecasting for Seemingly Unrelated Time Series: Application to Local Government Revenue Forecasting,”Management Science, 39(March), 275–93.
8.
EasingwoodChristopher J., MahajanVijay, and MullerEitan (1983), “A Nonuniform Influence Innovation Diffusion Model of New Product Acceptance,”Marketing Science,2(Summer), 273–95.
9.
GorrWilpen L., and HsuCheng (1985), “An Adaptive Filtering Procedure for Estimating Regression Quantiles,”Management Science, 31(August), 1019–29.
10.
HeelerRoger M., and HustadThomas P. (1980), “Problems in Predicting New Product Growth For Consumer Durables,”Management Science, 26(October), 1007–20.
11.
HorskyDan, and SimonLeonard S. (1983), “Advertising and the Diffusion of New Products,”Marketing Science,2(Winter), 1–17.
12.
JainDipak C., and RaoRam C. (1989), “Effect of Price on the Demand for Durables: Modeling, Estimation and Findings,”Journal of Business and Economic Statistics, 8(April), 163–70.
13.
JohnstonJohn (1984), Econometric Method.New York: McGraw-Hill Book Company.
14.
KahlDouglas R., and LedolterJohannes (1983), “A Recursive Kalman Filter Forecasting Approach,”Management Science, 29(November), 1325–33.
15.
KalishShlomo (1983), “Monopolist Pricing With Dynamic Demand and Production Cost,”Marketing Science, 2(Spring), 135–60.
16.
KalishShlomo (1985), “A New Product Adoption Model with Pricing, Advertising and Uncertainty,”Management Science, 31(December), 1569–85.
17.
LedolterJohannes, and KahlDouglas R. (1984), “Adaptive Filtering: An Empirical Evaluation,”Journal of the Operational Research Society, 35(4), 337–45.
18.
LenkPeter J., and RaoAmbar G. (1990), “New Models From Old: Forecasting Product Adoption by Hierarchical Bayes Procedures,”Marketing Science, 9(Winter), 42–53.
19.
LewisL. Frank (1986), Optimal Estimation.New York: John Wiley & Sons.
20.
LilienGary L., RaoAmbar G., and KalishShlomo (1981), “Bayesian Estimation and Control of Detailing Effort in a Repeat Purchase Diffusion Environment,”Management Science, 27(May), 493–506.
21.
MahajanVijay, MasonCharlotte H., and SrinivasanV. (1986), “An Evaluation of Estimation Procedures for New Product Diffusion Models,” in Innovation Diffusion Models of New Product Acceptance, MahajanVijay, and WindJerry, eds. Cambridge, MA: Ballinger Publishing Co.,203–32.
22.
MahajanVijay, MullerEitan, and BassFrank M. (1990), “New Product Diffusion Models in Marketing: A Review and Directions for Research,”Journal of Marketing, 54(January), 1–26.
23.
MahajanVijay, and SharmaSubhash (1986), “A Simple Algebraic Estimation Procedure for Innovation Diffusion Models of New Product Acceptance,”Technological Forecasting and Social Change, 30(December), 331–46.
24.
MeadeNigel (1985), “Forecasting Using Growth Curves: An Adaptive Approach,”Journal of the Operational Research Society, 36, 1103–15.
25.
MorrisonG. Wayne, and PikeDavid H. (1977), “Kalman Filtering Applied to Statistical Forecasting,”Management Science, 23(March), 768–78.
26.
NortonJohn A., and BassFrank M. (1987), “A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products,”Management Science, 33(September), 1069–86.
27.
SchmittleinDavid C., and MahajanVijay (1982), “Maximum Likelihood Estimation for an Innovation Diffusion Model of New Product Acceptance,”Marketing Science, 1(Winter), 57–78.
28.
SimonHerman, and SebastianKarl-Heinz (1987), “Diffusion and Advertising: The German Telephone Campaign,”Management Science, 33(April), 451–66.
29.
SladeMargaret E. (1989), “Modeling Stochastic and Cyclical Components of Technical Change,”Journal of Econometrics, 41, 363–83.
30.
SrinivasanV., and MasonCharlotte H. (1986), “Nonlinear Least Squares Estimation of New Product Diffusion Models,”Marketing Science, 5(Spring), 169–78.
31.
StengelRobert F. (1986), Stochastic Optimal Control: Theory and Application.New York: John Wiley & Sons.
32.
SultanFareena, FarleyJohn U., and LehmannDonald R. (1990), “A Meta-Analysis of Application of Diffusion Models,”Journal of Marketing Research, 27(February), 70–77.
33.
TegeneAbebayehu (1990), “The Kalman Filter Approach for Testing Structural Change in the Demand for Alcoholic Beverages,”Applied Economics, 22, 1407–16.
34.
TegeneAbebayehu (1991), “Kalman Filter and the Demand for Cigarettes,”Applied Economics, 23, 1175–82.
35.
WildtAlbert R., and WinerRussell S. (1983), “Modeling and Estimation in Changing Market Environments,”Journal of Business, 56(July), 365–88.
36.
XieJinhong, and SirbuMarvin A. (1995), “Price Competition and Compatibility in the Presence of Network Externalities,”Management Science, 41(May) 909–26.
