Modeling Financial Market States with Markov Chains
Summary
The article introduces Markov chains as probabilistic models for transitions among defined states. It explains the transition matrix and the memoryless assumption: the next state depends on the current state and elapsed time, rather than the full path taken to reach it. It distinguishes discrete-time and continuous-time chains and also discusses hidden and switching variants, while noting that transition probabilities can be estimated from observed data using methods such as maximum likelihood or expectation maximization.
For financial use, the proposed idea is to define market states and estimate how often transitions occur, then use those probabilities to reason about possible future states. The article mentions a daily EURJPY test for 2022, but the supplied text omits the report details, so the results cannot be assessed here. It cautions that time-homogeneous assumptions may be unsuitable when transition behavior changes, and that chains may be a poor fit for data with many states or complex dependencies. The discussion does not establish predictive performance or profitability.
Key ideas
- A Markov chain represents transitions among states with probabilities organized in a transition matrix.
- The model assumes that future transitions depend on the current state, not the full history.
- Transition probabilities can be estimated from observed transitions using maximum likelihood or expectation maximization.
- Market states must be defined before applying a chain to financial time series.
- Time-varying transition behavior and complex state structures can limit the model’s usefulness.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.