States and observations in a HMM for FX markets

Question

I would like to set up a hidden Markov model (HMM) for foreign exchange (FX) markets. To start with, I am thinking of a model that only has three states "up", "down" and "flat" (within some range from previous close). The states are compared to previous day's closing price. How would one model this?

In general, there are no hidden states in the market. I can observe prices all time periods. If I use every single price as an observation, that would leave me with a lot of observations to map into only three states. I'm wondering if that will cause some issues. I would at least expect some sort of normalisation of the prices to be needed in this case. Alternatively, observations and are also mapped into these three states, but wouldn't that leave me with identical transition and emission matrices?

Basically, how do you model states and observations in financial markets, when you can observe it all?

It's OK to try to replicate Rentec but you're probably not the first one to try! — PC1, Jul 11 '22 at 17:20
@PC1 well, I never said that and I'm pretty sure they do something much more advanced. This is really more for the fun of it. Of course, if I can become a billionaire on it, I'll take it. — Thomas Hemming Larsen, Jul 12 '22 at 10:40
The hidden states could be the "market regimes", i.e., the state of psychosis of the market players. — Rodrigo de Azevedo, Dec 27 '23 at 12:01
https://quant.stackexchange.com/questions/tagged/hidden-markov-model — Rodrigo de Azevedo, Dec 27 '23 at 12:08

score 2 · Answer 1 · answered Jul 11 '22 at 17:18

You're basically getting at the heart of the problem in all tracking and estimation applications: How good is your model of the stochastic process, and thus, how much can you infer from the modeling assumptions?

In your example, you're basically making the modeling assumption that the market exists in one of only 3 possible states (going up, staying put, or going down). I can see this maybe being a useful model in some cases, but it's extremely simplistic.

To answer your main question, the assumption with a HMM is that your states are hidden and your observations are random. That is, in your model, it would be possible for the market to truly be in the "going up" state, but for you to observe a price decrease in some particular stock.

The problem with the stock market in general though, is that a realistic model of it is infinitely complex. There are in fact infinite unobservable states that the entire market apparatus could be in.

Thanks! Perhaps a clarification, I'm not trying to say whether the market is trending up or down, only if the next day's price will be higher or lower than the current. So I'm not saying that the observations come from different distributions depending on trend in the market. — Thomas Hemming Larsen, Jul 12 '22 at 07:14

States and observations in a HMM for FX markets

1 Answers1