3-State, Input, Duration, and Factorial HMM Guide

Hera vs Metis: pure price returns vs external context inputs

Hera (included in Free) is the classic three-state hidden Markov model: it looks strictly at the asset’s own return series to infer bull, chop, and bear probabilities. Because Hera estimates relatively few parameters, it converges fast on short lookback windows and serves as the clean control experiment for every asset.

Metis (unlocked in Plus) is an input-aware HMM—often called an input-output HMM in statistical literature. Instead of assuming regime transitions happen in a vacuum, Metis conditions state behaviour on external features such as on-device FinBERT headline sentiment and synced context agents like Kronos CPI inflation or Zeus S&P 500 readings.

• Hera (Free): classic 3-state price-only HMM; fast baseline with minimal overfitting surface.
• Metis (Plus): input-aware HMM that incorporates synced macro, seasonal, and on-device sentiment series.
• Hestia (Plus): explicit duration-aware HMM designed to curb rapid one-bar state flickering.
• Athena (Pro): factorial HMM tracking multiple hidden regime layers simultaneously.

Hestia: modelling how long a crypto regime tends to last

In a standard Markov chain, the implied dwell time inside any state follows a geometric distribution—meaning the highest single-bar exit probability occurs immediately after entering the state. On noisy hourly or daily crypto bars, that geometric memorylessness can cause rapid state chatter during choppy weeks.

Hestia (Plus) introduces duration awareness (akin to hidden semi-Markov structure), explicitly modelling how many bars a trend or consolidation typically persists before switching. When historical trends on a pair tend to run for multi-week stretches, Hestia penalises premature flip-flopping caused by a single counter-trend candle.

Athena: separating layered regimes with a factorial HMM

Markets rarely have just one hidden dimension: directional trend (up vs down) and volatility environment (calm compression vs violent expansion) can shift on independent clocks. A calm grind higher behaves very differently from a parabolic blow-off top, even though both print positive average drift (mu).

Athena (Pro) implements a factorial hidden Markov model that decomposes latent market state across parallel chains—allowing directional posture and volatility layering to evolve together without exploding a single transition matrix into dozens of sparse states.

Test model complexity systematically without fooling yourself

More parameters do not automatically produce a better simulation; on short five-minute histories, a complex model can memorise noise that a three-state baseline ignores. Compare the four architectures using controlled one-variable steps.

Keep every other setting fixed while rotating models on the same Binance USDT asset.

1. Fix your asset, bar interval, start date, window length, and iteration budget, then run Hera first to record the baseline equity curve and regime switches.
2. Switch to Hestia without enabling extra signals to isolate whether explicit regime duration reduces whipsaw trades during sideways ranges.
3. Sync your chosen context agents and test Metis to observe whether external macro or sentiment inputs shift transition timing meaningfully.
4. Evaluate Athena on longer daily or multi-month histories where layered volatility and trend states have enough bars to estimate cleanly.