Identification of Volatility Regimes in Financial Time Series Using Mixture Models, Markov Processes, and Bayesian Updating
Faculty Mentor Information
Paul Bartell, University of Idaho
Presentation Date
7-15-2026
Abstract
Most of the real-world dynamic data do not have uniform relationships over time. Instead, they alternate between periods of stability and high variability. The financial market and its performance are the best examples of this phenomenon. These evolving changes are described as volatility regimes, or market behaviors where statistical properties of the signal differ across time intervals. Traditional statistical models backed by traditional financial models such as GARCH capture changing variance using a fixed set of assumptions, whereas today's machine learning models can detect structural patterns but lack the idea of explanation of probabilities, direction and interpretation of how different market regimes rotate within the overall market itself. This study proposes a unified framework for identifying distinct volatility regimes in financial time series. The framework combines: 1. Gaussian Mixture Models (GMM) to detect latent clusters in volatility data, 2. Hidden Markov Models (HMM) to model transitions between regimes, and Bayesian updating to continuously revise regime probabilities as new observations arrive. The goal is to determine whether volatility states can be statistically separated, whether transitions between them follow a Markov structure, and whether adaptive probabilistic updating improves state inference. This research develops a quantitative approach of identifying correct regimes to avoid misapplication of uncertain strategies.
Identification of Volatility Regimes in Financial Time Series Using Mixture Models, Markov Processes, and Bayesian Updating
Most of the real-world dynamic data do not have uniform relationships over time. Instead, they alternate between periods of stability and high variability. The financial market and its performance are the best examples of this phenomenon. These evolving changes are described as volatility regimes, or market behaviors where statistical properties of the signal differ across time intervals. Traditional statistical models backed by traditional financial models such as GARCH capture changing variance using a fixed set of assumptions, whereas today's machine learning models can detect structural patterns but lack the idea of explanation of probabilities, direction and interpretation of how different market regimes rotate within the overall market itself. This study proposes a unified framework for identifying distinct volatility regimes in financial time series. The framework combines: 1. Gaussian Mixture Models (GMM) to detect latent clusters in volatility data, 2. Hidden Markov Models (HMM) to model transitions between regimes, and Bayesian updating to continuously revise regime probabilities as new observations arrive. The goal is to determine whether volatility states can be statistically separated, whether transitions between them follow a Markov structure, and whether adaptive probabilistic updating improves state inference. This research develops a quantitative approach of identifying correct regimes to avoid misapplication of uncertain strategies.