Assessment of model adequacy for Markov regression time series models

In Markov regression models with time series data, we apply asymptomatic results to obtain the quasi-score, quasi-Wald, and quasi-likelihood ratio tests for assessing model adequacy. Based on limited simulation studies, we show that these three test statistics, particularly the quasi-score test, perform reasonably well in small samples. In addition, we apply these tests to the mean-shift outlier model to examine outliers. The usefulness of these tests is demonstrated via the analysis of three practical examples.