The Estimation of Nonstationary Transition Probabilities

Warren Dent
Additional contact information
Warren Dent: University of Iowa

Management Science, 1973, vol. 20, issue 3, 308-312

Abstract: The estimation of an underlying Markov process of constant transition probabilities which explains aggregated market share movements over time has received much attention from theorists and applied researchers. Summaries of the work to date are given in [Dent, Warren T., Richard Ballintine. 1971. A review of the estimation of transition probabilities in Markov chains. Australian J. Agricultural Econom. 15 and Lee, T. C., G. G. Judge, A. Zellner. 1970. Estimating the Parameters of the Markov Probability Model from Aggregate Time Series Data. North-Holland, Amsterdam.]. The problem of estimating a nonstationary process however has not been solved, although Hallberg [Hallberg, M. C. 1969. Projecting the size distribution of agricultural firms--an application to a Markov process with non-stationary transition probabilities. J. Farm Econom. 51.] has looked at the problem in the case of micro data, that is, when movements between periods are observable. Harary, Lipstein, and Styan [Harary, F., B. Lipstein, G. P. H. Styan. 1970. A matrix approach to nonstationary chains. Oper. Res. 18.] have investigated nonstationary chain properties in the case of aggregated data but have not looked at estimation. We present an attempt to formalize Harary, Lipstein, and Styan's model and to develop appropriate solution techniques for estimation of its unknown parameters. An iterative quadratic programming procedure is suggested.

Date: 1973
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.20.3.308 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:20:y:1973:i:3:p:308-312

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().