Choosing Hidden States and Observations for Forex HMMs

Summary

The document explains that hidden Markov model states for foreign-exchange returns are modeling choices rather than fixed categories such as “hot” or “cold.” One possible setup assigns discrete states according to whether returns are positive or negative, with observed returns providing the data used to infer the hidden state. This is a simple classification scheme and requires deciding how to treat zero or near-zero returns if those occur.

An alternative is to use continuous emission distributions, with each hidden state associated with parameters such as a mean and variance. An observed return can then have some probability under each state, with inference favoring the state whose distribution best fits it. The answer is conceptual and does not specify a complete model, data frequency, state count, fitting procedure, or evidence of predictive performance. Those choices must be set and evaluated for the particular currency pair and use case; identifying latent regimes alone does not establish useful forecasts.

Key ideas

• HMM states are latent categories that the modeler defines for the application.
• Positive and negative returns can serve as a basic discrete-state interpretation.
• Continuous emissions can associate each state with its own return mean and variance.
• An observed return may be plausible under multiple states, with likelihoods indicating relative fit.
• The document does not prescribe state count, estimation details, or a method for validating forecasts.

Tags

# When predicting Forex price using HMM what, typically, are the states and what are the observations?


# When predicting Forex price using HMM what, typically, are the states and what are the observations?












I understand their abstract definition but having trouble applying the HMM method to Forex prices. What should the observations be? Then what should the states be (like "hot", "cold", etc.)?

## Answer by xav (score 3, accepted)

https://quant.stackexchange.com/a/37389

Your decision. You can define the states to be "positive return" or "negative return". So if the return is negative, then its state would be that "negative return".

Or, you could even model them with continuous emission so as to define a state with a specific mu and variance. So that given the return at time T, you can say "it could technically be possible that this return be in any one of these states, but it's most likely that it's at this state given its mu and variance"

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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