An earlier version of this paper has circulated under the title “Optimal Test for Markov Switching.” The authors are grateful to an editor and three referees for helpful comments. Carrasco gratefully acknowledges partial financial support from the National Science Foundation under Grant SES-0211418.
Optimal Test for Markov Switching Parameters
Version of Record online: 1 APR 2014
© 2014 The Econometric Society
Volume 82, Issue 2, pages 765–784, March 2014
How to Cite
Carrasco, M., Hu, L. and Ploberger, W. (2014), Optimal Test for Markov Switching Parameters. Econometrica, 82: 765–784. doi: 10.3982/ECTA8609
- Issue online: 1 APR 2014
- Version of Record online: 1 APR 2014
- Manuscript received June, 2009; final revision received February, 2013.
- Information matrix test;
- optimal test;
- Markov switching model;
- Neyman–Pearson lemma;
- random coefficients model
This paper proposes a class of optimal tests for the constancy of parameters in random coefficients models. Our testing procedure covers the class of Hamilton's models, where the parameters vary according to an unobservable Markov chain, but also applies to nonlinear models where the random coefficients need not be Markov. We show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate. Therefore, standard approaches do not apply. We use Bartlett-type identities for the construction of the test statistics. This has several desirable properties. First, it only requires estimating the model under the null hypothesis where the parameters are constant. Second, the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function. We derive the asymptotic distribution of our test under the null and local alternatives. Asymptotically valid bootstrap critical values are also proposed.