Testing for a Markov-Switching Mean in Serially Correlated Data

Morley, James and Rabah, Zohra (2014) Testing for a Markov-Switching Mean in Serially Correlated Data. In: Recent Advances in Estimating Nonlinear Models. Springer, New York, pp. 85-97. ISBN 9781461480594

Abstract

When testing for Markov switching in mean or intercept of an autoregressive process, it is important to allow for serial correlation under the null hypothesis of linearity. Otherwise, a rejection of linearity could merely reflect misspecification of the persistence properties of the data, rather than any inherent nonlinearity. However, Monte Carlo analysis reveals that the Carrasco, Hu, and Ploberger (Optimal test for Markov Switching parameters, conditionally accepted at Econometrica, 2012) test for Markov switching has low power for empirically relevant data-generating processes when allowing for serial correlation under the null. By contrast, a parametric bootstrap likelihood ratio test of Markov switching has higher power in the same setting. Correspondingly, the bootstrap likelihood ratio test provides stronger support for a Markov-switching mean in an application to an autoregressive model of quarterly US real GDP growth.