Recursive Estimation in Switching Autoregressions With a Markov Regime

Abstract

A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. We propose a recursive algorithm for parameter estimation in a switching autoregressive process governed by a hidden Markov chain. A common approach to the recursive estimation problem is to base the estimation on suboptimal modifications of Kalman filtering techniques. The main idea in this paper is to use the maximum likelihood method and from this develop a recursive EM algorithm.

Volatility regime-switching in European exchange rates prior to monetary unification

“…Obviously, it is the interaction between the regime-specific autoregressive parameters and the transition probabilities which determines the stationarity of the complete Markov-switching model. Karlsen (1990) and Holst et al (1994) suggest a sufficient condition according to which the Markov-switching model from Eqs. (2)-(10) is weakly stationary if the (2 Â 2) matrix…”

Real exchange rates and switching regimes

“…Note that this stationarity condition implies that it is the interaction between the autoregressive parameters and the transition probabilities that determines whether the variable x t is weakly stationary or not. It may well be the case that any of the two autoregressive parameters is greater than one and still the stationarity condition above is satisfied (see Holst et al, 1994). The intuition is that as long as there is a sufficiently high probability of switching from the explosive regime to a stationary regime, the whole model is stationary.…”

Short Rate Nonlinearities and Regime Switches

“…In a three-state model applied to interest rates from seven countries they find significant within-regime heteroskedasticity. Gray (1996) Holst et al (1994)). This makes regimeswitching models ideal models to capture the non-linearities of short rates.…”