Optimal Test for Markov Switching

Abstract

Comments welcome We propose a new class of tests for the stability of parameters. We cover the class of Hamilton models, where regime changes are driven by an unobservable Markov chain. We derive a class of information matrix-type tests and show that they are equivalent to the likelihood ratio test. Hence, our tests are asymptotically optimal. Moreover these tests are easy to implement as they do not require the estimation of the model under the alternative. They are also very general. Indeed, the underlying process driving the regime changes may have a finite or continuous state space, as long as it is exogenous. The model itself need not be linear. It may be a GARCH model, for instance. We use this test to investigate the presence of rational collapsing bubbles in stock markets. Using US data, we find evidence in favor of nonlinearities, which are consistent with periodically collapsing bubbles.

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