Statistical inference in nonstationary markov models with embedded explanatory variables

Abstract

In this paper, we develop an operational nonstationary Markov process model for use with macro aggregate frequency data. Independent, time-variant factors assumed to affect the process of interest are embedded in the model. Transition probabilities are estimated indirectly from the coefficients on the embedded variables. We previously concluded that either the Marquardt or the simplex, derivative-free nonlinear programming algorithm could be used to estimate such a model. Here, we propose a test for parameter stationarity. By means of designed simulation experiments for the two-state model, we find that our test has acceptable Type I error probabilities, and that power rises with the degree of departure from the null hypothesis. Both validity and power performance can be improved by longer time records of data and a greater number of entities observed.

Keywords:

• Nonstationary Markov process
• embedded variables
• least squares estimation
• test for stationarity
• experimental design
• Monte Carlo simulation