Hypothesis Tests for Markov Process Models Estimated from Aggregate Frequency Data

Abstract

When the only data available for estimating the transition probabilities of a Markov chain are state occupation frequencies (rather than interstate transition frequencies), a least squares estimation technique and an accompanying hypothesis-testing methodology are proposed. This general hypothesis-testing procedure is used to develop three tests for adequacy of the simple stationary model. Null hypotheses of a zero-order process, stationarity, and homogeneity are considered. The distributions of the test statistics are investigated in a factorially designed Monte Carlo study. In general, it is found that treating the test statistics as having F distributions with appropriate degrees of freedom under the null hypothesis of interest leads to rejection proportions close to the desired levels. Additional Monte Carlo results indicate favorable power of the proposed tests.

Key Words:

• Markov processes
• Estimation and testing
• Aggregate frequency data