Markov Chains and Hidden Markov Models for Price-State Forecasting

Summary

The article introduces Markov models, focusing on Markov chains and hidden Markov models (HMMs), and explains how they can represent random processes whose next state depends on the current state. A fully observable process can be modeled as a Markov chain; an HMM allows the underlying states to be hidden while their effects appear in observed data.

For a simple market example, the article labels daily SPY price movements as up, down, or flat, counts transitions between states, and converts those counts into a transition probability matrix. Repeated matrix multiplication projects state probabilities forward and eventually approaches an equilibrium distribution. The example outlines a modeling workflow, but provides no reported forecast accuracy or trading performance. Its state definitions are deliberately simple, and the Markov assumption may not capture dependencies on longer histories or changing market conditions. The article also points readers toward further HMM research and implementation material, while its downloadable code is not included in the text.

Key ideas

• A Markov chain models transitions among observable states using probabilities conditioned on the current state.
• A transition matrix can project the probabilities of future states through repeated multiplication.
• The example classifies daily SPY movements as up, down, or flat and estimates transitions from historical observations.
• An HMM represents a process whose underlying states are not directly observable.
• The article gives no evidence that its illustrative model produces profitable or accurate forecasts.

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