JUNIPER PUBLISHERS-Biostatistics and Biometrics Open Access Journal
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.
However, in this context, the use of
numerical procedures for finding point estimates and the related covariance
matrix are not efficient. In fact, point estimates are found by closed form
solutions. Consequently, having available an analytical calculation for the
covariance matrix casts doubts on the rationale of the application of numerical
procedures. They turn out not only to be inefficient with respect to their
analytical counterparts but also ineffective as they are based on
approximations.
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