Volatility forecasts in financial time series with HMM-GARCH models

Abstract

Nowadays many researchers use GARCH models to generate volatility forecasts. However, it is well known that volatility persistence, as indicated by the sum of the two parameters G1 and A1[1], in GARCH models is usually too high. Since volatility forecasts in GARCH models are based on these two parameters, this may lead to poor volatility forecasts. It has long been argued that this high persistence is due to the structure changes(e.g. shift of volatility levels) in the volatility processes, which GARCH models cannot capture. To solve this problem, we introduce our GARCH model based on Hidden Markov Models(HMMs), called HMM-GARCH model. By using the concept of hidden states, HMMs allow for periods with different volatility levels characterized by the hidden states. Within each state, local GARCH models can be applied to model conditional volatility. Empirical analysis demonstrates that our model takes care of the structure changes and hence yields better volatility forecasts. © Springer-Verlag Berlin Heidelberg 2004.