STATISTICAL FRAMEWORKS FOR PRICE DYNAMICS ANALYSIS: THE EFFICACY OF HMM AND HSMM

In order to make reliable financial predictions, one must be able to accurately predict how prices will change in extremely volatile markets, such as Bitcoin. In order to enhance prediction accuracy, this study presents a hybrid model that combines the two prominent statistical approaches, the Hidden Semi-Markov Model (HSMM) and the Hidden Markov Model (HMM). As a stochastic framework, the HMM connects visible price changes to a hidden state. A probability matrix captures the temporal linkages evident in price dynamics by describing transitions between states. Emission probabilities govern the possibility of seeing specific prices linked with these concealed states and improve the association between states and actual prices. On the flip side, the HSMM improves upon the HMM by adding duration dependencies, which let states have different durations. A state duration distribution enables this feature, which in turn gives more information about the time-varying nature of prices. Across a range of error metrics, our data shows that the HSMM performed better than the HMM. Notably, the HSMM attained an MAE of 0.0246, an MSE of 0.0014, and an RMSE of 0.0372. When compared, the HMM achieved RMSE is 0.0672, MAE is 0.0446, and MSE is 0.0514. Cryptocurrency markets are notoriously volatile, and these results show that the HSMM does a better job of accounting for non-linear behaviors and temporal variability.