A Maximum-Entropy Markov-Switching GARCH Framework for Cryptocurrency Volatility Regime Detection and Forecasting

The distributional specification in Markov-switching GARCH models has historically been driven by empirical convention rather than statistical theory. This paper derives the two-regime MS-GARCH specification from the Maximum Entropy Principle, providing an information-theoretic motivation for Student-t regime-conditional innovations in cryptocurrency volatility modelling. The framework is applied to five major cryptocurrencies, Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash, over the period January 2017 to March 2026, comprising 15,834 daily observations spanning six complete market cycles. Three principal findings emerge. First, a Calm-Phase Fragility pattern is identified: four of five assets exhibit calm-regime half-lives below one trading day (0.48 to 1.16 days), with turbulence the dominant long-run state (stationary turbulent probability in [0.451, 0.771] across all assets), establishing turbulence rather than calm as the structural baseline of the cryptocurrency ecosystem. Second, the Maximum Entropy derivation yields endogenous Student-t degrees of freedom, with heavy-tailed turbulent innovations (degrees of freedom approximately 4.5) confirmed across all assets, validating the MaxEnt constraint framework empirically. Third, near-unity turbulent GARCH persistence drives MS-GARCH point forecasts toward the persistence ceiling, consistent with an information-theoretic bound on predictability when the calm half-life collapses below one trading day; HAR-RV achieves the lowest QLIKE loss for three of five assets under these near-critical conditions. Cross-asset consistency is confirmed across seven statistical indicators including Hill tail exponents in [2.31, 3.26], Hurst exponents in [0.543, 0.577], and Wald tests rejecting parameter homogeneity at p < 0.001 for all assets. The framework is formalised as a deployable expert system for real-time regime monitoring and risk management.