ABSTRACT : This paper performs an in-depth empirical study on the application of advanced probabilistic and statistical models to analyze the volatility behavior of the cryptocurrency market during the 2024-2026 strategic transition. The core research focus lies in combining the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) framework with Markov Switching (MS) models to identify unobservable market regimes, ranging from low-stability zones to extreme turbulence. Utilizing daily time-series data for Bitcoin and Ethereum from 2020 to March 2026, the study applies a modern data analysis pipeline in Python, including unit root testing, parameter estimation via Maximum Likelihood Estimation (MLE), and volatility forecasting using expanding rolling windows. The novelty of this research stems from the application of the Maximum Entropy (MaxEnt) principle to endogenously determine innovation distributions and analyze the impact of institutionalization—specifically through Spot ETF approvals, the establishment of the U.S. Strategic Bitcoin Reserve (SBR), and the geopolitical shocks of early 2026. Empirical results indicate that the MS-GARCH model with Student-t distributions significantly outperforms traditional models in explaining "fat-tail" phenomena while identifying the "Calm-Phase Fragility Law," where market stability becomes increasingly susceptible to macro-liquidity variables. Economic analysis suggests that digital assets have integrated into global financial infrastructure, necessitating risk management frameworks based on high-sensitivity, adaptive probabilistic modeling.
Nguyễn Thị Phương Dung (Tue,) studied this question.