Hidden Markov modelling of time series variance regimes using large deviation theory

Abstract

Heteroskedasticity occurs when the variance of a time series fluctuates. This alters the distribution and modeling of the series. Volatility models such as GARCH and ARCH have demonstrated insufficiency in modeling such series. The shortcomings of the models have led to the development of regime-switching volatility models, which have demonstrated efficacy in modeling such series. Markov switching volatility models exhibit greater efficiency by integrating regime dependencies in the modeling of regime transitions. Nevertheless, the models depend on precise identification and modeling of the fundamental Markov chain that governs the variance regimes. The maximum likelihood estimation (MLE) and expectation maximization (EM) have been used before to model the hidden Markov regimes of such series. This study presents an alternative approach for modeling Hidden Markov Models (HMM) through the Large Deviation Principle (LDP). The approach employed LDP to ascertain variance regimes and MLE to estimate HMM parameters. The Viterbi algorithm decodes the series’ variance regimes after estimating the model parameters. We juxtaposed the model results with those of the Expectation Maximization Hidden Markov Model (EM-HMM). The two methods yielded nearly identical sets of variance regimes for heteroscedastic time series, as demonstrated by the simulations and the gold price data. We determined that the model surpassed the EM algorithm in discerning the number of underlying variance regimes. The approach was more effective for modeling the underlying variance regimes when the EM algorithm did not converge. It also proved more effective for modeling the fundamental variance regimes relative to a benchmark variance.