Markov Switching Models for Volatility : Filtering, Approximation and Duality

This paper is devoted to show duality in the estimation of Markov Switching (MS) processes for volatility. It is well-known that MS-GARCH models suffer of path dependence which makes the estimation step unfeasible with usual Maximum Likelihood procedure. However, by rewriting the MS-GARCH model in a suitable linear State Space representation, we are able to give a unique framework to reconcile the estimation obtained by the Kalman Filter and with some auxiliary models proposed in the literature. Reasoning in the same way, we present a linear Filter for MS-Stochastic Volatility (MS-SV) models on which different conditioning sets yield more flexibility in the estimation. Estimation on simulated data and on short-term interest rates shows the feasibility of the proposed approach