Econometrica: Jul 2012, Volume 80, Issue 4

Testing for Regime Switching: A Comment

https://doi.org/10.3982/ECTA9622
p. 1809-1812

Andrew V. Carter, Douglas G. Steigerwald

An autoregressive model with Markov regime‐switching is analyzed that reflects on the properties of the quasi‐likelihood ratio test developed by Cho and White (2007). For such a model, we show that consistency of the quasi‐maximum likelihood estimator for the population parameter values, on which consistency of the test is based, does not hold. We describe a condition that ensures consistency of the estimator and discuss the consistency of the test in the absence of consistency of the estimator.
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Supplemental Material

Supplement to "Testing for Regime Switching: A Comment"

In this supplemental section we prove that, for an autoregressive process, the gradient of the quasi-log-likelihood does not equal zero when evaluated at the popluation parameter values.

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