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Specification testing for Markov switching model

Posted: Mon Jan 16, 2023 4:46 pm
by fr4014
Ideally, one would like to test the null hypothesis that m 5m and s 5 s . The implication of finding this would be that the Markov switching model had been unable to separate out the data into two distinct regimes; in other words, that it is possible to restrict the data to be
as drawn from only one regime. Unfortunately, as Engel and Hamilton (1990) point out, the derivative of the likelihood function with respect to mu 1 and mu 2 is zero, and the information matrix is singular under the null so that the usual regularity conditions for the asymptotic validity of the hypothesis tests do not hold. Engel and Hamilton (1990) suggest testing this hypothesis indirectly by considering the following two slightly more general hypotheses

rest of the description is attached in the image 1

Test results reported by author is attached in image 2 and his interpretation is reported in image 3.

I would like to know how to find the W1 and W2 values that he reported in table after the estimation of markov switching model.