Regime Characteristics Parameter Estimation of Hidden Markov Model on Time Series Data

Abstract

The hidden Markov model (HMM) is a versatile and well-adapted method for sequential data analysis. It is often adopted to study occurrences where one part of the phenomenon is visible or observable while the other is hidden or unobservable. Markovswitching models are stochastic processes that switch between regimes or states. The
switching between the states works on the assumption that the unobserved states depend on a Markov chain. Regime-switching models are suitable for modeling economic time series where the dynamics are characterized differently within periods. These periods could, for example, be periods of financial stability versus periods of financial volatility or periods of economic expansion versus economic recession. Many classical time series
models depend on a single set of model parameters that are assumed to be adequate for modeling the dynamics of time series data over these different periods. But another opinion maintains that this classical model assumption is not always logical for real-life data, where time-series data may have varying characteristics, such as the means and variances across these different periods, hence is better modeled using regime-switching models. This work explored the parameter estimation of a hidden Markov model with application to stock price time series using the maximum likelihood estimation method. The results showed different mean and variance values in the four regimes used for the analysis. The findings indicate that regime-switching models may outperform single models in capturing the empirical characteristics of financial time series data.