What is a Hidden Markov Model and how is it used to detect market regimes?

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AcadiFi · Accepted Answer

A Hidden Markov Model (HMM) is a doubly stochastic process: an unobserved state sequence S_t evolving by a Markov chain, and an observed emission y_t drawn from a state-specific distribution...

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Three core problems define HMM usage: (1) Evaluation — compute the likelihood of an observed sequence given parameters using the forward algorithm. (2) Decoding — find the most likely state sequence given observations using the Viterbi algorithm. (3) Learning — estimate transition probabilities, initial distribution, and emission parameters using Baum-Welch (an EM variant).

At Hollowmere, suppose Bitcoin daily log-returns are modeled with a 3-state Gaussian HMM: calm, volatile, crash. After Baum-Welch converges on two years of data, you might observe transition probabilities like P(calm->volatile) = 0.08 and P(crash->crash) = 0.72, meaning crashes cluster.

For trading signals, Viterbi gives an offline optimal path but uses future data. For real-time tactical overlays, you'd use forward-filtered probabilities P(S_t = k | y_{1:t}). An AcadiFi practitioner note: emission distributions don't have to be Gaussian; you can use Student-t for fat tails, or even switch the entire volatility process per state. Choose K carefully — BIC or cross-validated predictive log-likelihood beats in-sample AIC for this class of models.

What is a Hidden Markov Model and how is it used to detect market regimes?

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