HMM AND HSMM IN TIME SERIES

Анотація

The main focus of the work is on the study of so-called hidden Markov chains (hidden Markov models, HMM) and their analogs and generalizations. In particular, the research examines the impact of HMM and semi-Markov hidden models (HSMM) on time series models describing the stock prices of top companies as of 2024. The study revealed that considering more generalized models allows for a more accurate description of stock price dynamics and, consequently, a more accurate determination of the key characteristics of the actual process. The research employs both HMM and HSMM frameworks to analyze financial data, demonstrating their capacity to capture key features of stock price volatility, including sharp transitions between periods of high and low market variability. A series of tests and metrics were conducted to evaluate the performance of these models, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), which indicate superior fit for HSMMs. Additionally, methods such as the Augmented Dickey-Fuller (ADF) test and KPSS tests were used to validate the stationarity properties of the time series. The study's results emphasize that semi-Markov extensions provide a significant improvement over classical HMMs when analyzing financial market data, allowing for better detection of long-term dependencies and accurate modeling of asset price trends. The findings open avenues for further applications in financial risk analysis and forecasting tasks, showcasing the potential of HSMMs to deliver more robust insights into market behavior.

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