Hidden Markov Models

Hidden Markov models have been proven successful for speech recognition, and their success carries over to the prediction of financial time series. According to Patterson's The Quants, and Mallaby's More Money Than God, Renaissance Technologies owes a great deal of their success to hidden Markov models. Research by academics in this paper and this other paper further validated the financial utility of hidden Markov models, and papers such as this one demonstrated their superiority over GARCH(1, 1) models for accurate volatility modeling.

The major issue with using hidden Markov models to predict financial time series is that we are trying to forecast the inherently chaotic. Put differently, forcing HMMs to learn from raw financial data is not always the best idea because it forces them to learn to try and predict the outcome of Brownian motion. On the other hand, that's what information theory is supposed to be about--detecting and predicting signals through a 'noisy' passageway. So while HMMs can still certainly be used on financial data, it's a bit much to ask. The one glaring exception to this is the use of high frequency data, which contains more data and hence is more likely to contain some pattern or other that daily or longer-term data does not reveal. So if dealing with daily or longer-term data, it's a lot easier to do something that eliminates market noise and results in a more statistically calm, pattern-containing time series. Some such methods for hidden Markov models include statistical arbitrage, volatility arbitrage, correlation forecasting, and volume prediction.

Of course, HMMs can also be used even less directly; for instance, by doing information extraction--getting pure information from humans' news articles, such as those on Reuters.com. (My next post will discuss this briefly, and the one after that will talk about other information extraction methods.)

But the most fruitful, direct application of HMMs is in high frequency trading. Because they inherently sort returns into groups (with observations of these returns corresponding to certain probability distributions) that are the underlying 'states,' hidden Markov models can separate out statistically different price movements the same way they can distinguish between vowels and consonants in a two-state model. Put differently, the way underlying states fit together with each other means that even if observed returns are uncorrelated with each other across time, they may be related in a more subtle way: one single certain type of return may be followed by another certain type of return more often than by returns not belonging to that type. I'll leave the rest up to the reader's imagination and programming skills.