Hidden Markov Models, Kalman Filtering, and Regime Decoding

Summary

The article introduces hidden Markov models as a way to infer unobserved states from observed data. It explains the Markov property, transition probabilities, and time-homogeneous chains, then relates hidden-state estimation to the Kalman filter’s prediction and measurement updates. It also outlines decoding: the Viterbi algorithm uses initialization, recursion, termination, and backtracking to find the most likely hidden-state sequence, while Baum-Welch is mentioned for estimating model parameters.

A financial example applies a two-state model to monthly G7 returns, interpreting states as low- and high-volatility regimes. The reported study finds differing persistence across countries, including longer high-volatility persistence in Japan and quicker exits in the United States. The treatment is introductory: key equations and tables are absent from the supplied text, and the author postpones detailed derivations and advanced algorithms. The example is descriptive and does not establish a trading strategy or predictive performance.

Key ideas

• A hidden Markov model links observed measurements to an unobserved state process.
• The Markov assumption makes the next hidden state depend on the current state rather than the full history.
• The Kalman filter provides an intuitive comparison for estimating latent processes from noisy observations.
• The Viterbi algorithm decodes the single most likely sequence of hidden states from observed data.
• A cited G7 application interprets two hidden states as low- and high-volatility regimes.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.