Friday, January 11, 2019

The Analytical Covariance Matrix for Regime - Switch in Models



Authored by Andrea Beccarini

This letter provides an analytical solution for the covariance matrix related to the (mean) parameters of the standard Markov-switching model. The importance of avoiding numerical procedures to estimate this matrix is also highlighted. Simulations are also performed in order to verify, in small samples, the actual advantage of the analytical formula. The seminal paper of Hamilton [1] provides a very attractive way to estimate regime-switching parameters of a model where the latent variable governing the regime switching enters the model without its lags. In this case, closed form solutions for these estimates are available. Surprisingly, Hamilton and the subsequent applied and theoretical literature do not consider a closed form solution for the related covariance matrix. Thus, the covariance matrix is generally found by numerical procedures whose aim is generally to estimate both the point Markov- switching (M-S) estimates and their covariance matrix in the maximum likelihood (ML) framework.


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