Markov Switching GARCH Models: Filtering, Approximations and Duality

Abstract

This paper is devoted to show duality in the estimation of Markov Switching (MS) GARCH processes. 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 model in a suitable state space representation, we are able to give a unique framework to reconcile the estimation obtained by filtering procedure with that coming from some auxiliary models proposed in the literature. Estimation on short-term interest rates shows the feasibility of the proposed approach.

Spectral analysis of Markov switching GARCH models with statistical inference

“…Results concerning stationarity, consistency of maximum likelihood (ML) estimates, geometric ergodicity, ‐structure, filtering, duality and statistical inference of univariate MS GARCH models can be found in Francq et al (2001), Francq and Zakoïan (2005), Liu (2006), Abramson and Cohen (2007), Xie (2009), Bauwens et al (2010), Billio and Cavicchioli (2017), and Augustyniak et al (2018). Francq and Zakoïan (2008) describe a procedure for computing the autocovariances and the ARMA representations of the squares, and higher‐order powers, of univariate MS GARCH models, with applications to statistical inference.…”