Identification-robust moment-based tests for Markov-switching in autoregressive models

TL;DR

This paper introduces robust moment-based tests for detecting Markov-switching in autoregressive models, overcoming identification issues of likelihood-based methods, and demonstrates their effectiveness through simulations and an empirical U.S. output growth analysis.

Contribution

It develops identification-robust, moment-based tests for Markov-switching in autoregressive models, offering a computationally simple alternative to likelihood-based methods.

Findings

Tests exhibit high power compared to existing methods.

Tests are computationally simple and robust to identification failures.

Empirical application demonstrates practical usefulness.

Abstract

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based inference methods. The approach exploits the moments of normal mixtures implied by the regime-switching process and uses Monte Carlo test techniques to deal with the presence of an autoregressive component in the model specification. The proposed tests have very respectable power in comparison to the optimal tests for Markov-switching parameters of Carrasco, Hu and Ploberger (2014} and they are also quite attractive owing to their computational simplicity. The new tests are illustrated with an empirical application to an autoregressive model of U.S. output growth.