Parameter Estimation in a Regime-Switching Model with Non-normal Noise

Abstract

This paper deals with the estimation of a Markov-modulated regime-switching model for asset prices, where the noise term is assumed non-normal consistent with the well-known observed market phenomena that log-return distributions exhibit heavy tails. Hence, the proposed model augments the flexibility of the current Markov-switching models with normal perturbation whilst still achieving dynamic calibration of parameters. In particular, under the setting where the model’s noise term follows a t-distribution, we employ the method of change of reference probability measure to provide recursive filters for the estimate of the state and transition probabilities of the Markov chain. Although recursive filters are no longer available for the maximum likelihood estimation of the model’s drift and volatility components under the current extension, we show that such estimation is tantamount to solving numerically a manageable system of nonlinear equations. Practical applications with the use of simulated and real-market data are included to demonstrate the implementation of our proposed algorithms.