A Markov-switching approach to modelling different volatility regimes

Abstract

In the past decades, the analysis and forecasting of volatility has received great attention, especially when modelling the conditional variances of the returns from financial time series data. Various discrete-time models have been proposed for this purpose, the most famous being ARCH and GARCH. However, due to the high persistence in their structure, these single-regime models often overestimate the conditional variance. The purpose of this thesis is to expand onto GARCH models which incorporate Markov-switching, hence allowing the model to switch between different regimes. Predominantly, Markov-switching GARCH has the ability to address the overestimation of volatility persistence after a shock. This thesis investigates the properties and inference of the Haas-Mittnik-Paolella Markov-switching model. This model is estimated using maximum likelihood estimation through a recursive filter and also using Bayesian framework through MCMC. The application involves fitting the single-regime models and the Markov-switching models to two financial time series data: New York Harbor heating oil and Bitcoin/USD exchange rate. The predictive performance is also analysed using risk management tools such as value at risk and expected shortfall.