| Regime analytics | regime_analysis | Statistics of any returns series by regime (return, volatility, ratio, spells and their compounded returns, empirical transitions) and transition-matrix analytics (stationary distribution, expected durations, half-lives, mixing, h-step forecast, simulated regime paths). | 2 |
| Discrete regime models | regime_discrete | Hidden Markov models on symbols and counts: categorical (coded series, return buckets, down/flat/up days; maximum likelihood or variational), Poisson (counts such as large moves, trades or defaults per period) and multinomial (counts over categories per period). | 3 |
| Gaussian regime models | regime_gaussian | Hidden Markov models with Gaussian, Gaussian-mixture or variational Gaussian emissions on returns or feature tables: regimes labelled by volatility or mean, transition matrix, per-regime means and volatilities, state path and probabilities, AIC/BIC, convergence, forecast and the fitted model. | 3 |
| Apply a fitted regime model | regime_inference | Use data.model of a regime fit without refitting: decode new or recent data into regimes with smoothed or real-time filtered probabilities, score it (log-likelihood, AIC/BIC, emission densities), and simulate regime scenarios. | 2 |
| Number of regimes | regime_selection | Choose how many regimes the data supports: a model family fitted across a range of state counts with random restarts, compared by BIC, AIC, log-likelihood, variational lower bound or held-out log-likelihood; the winning model is returned ready for regime_decode and regime_simulate. | 1 |
