Hidden Markov Models: Part II

Since hidden Markov models help researchers to find what sorts of observations tend to come after other types of observations, we have a situation where we can forecast stock behavior once we know what hidden state the security/commodity/currency/synthetic time series was most recently in. (By a synthetic time series, I mean some type of hedged position with a single value being bet on; cointegration residuals in statistical arbitrage, implied volatilities after delta hedging, and PCA-derived risk factor values.)

To successfully deploy capital using an HMM-driven technique, one needs to avoid overfitting the model to the data. I struggled with this. Closing prices from each day turned out to be too unpredictable to work, because the more time passed, the less the older patterns mattered; consequently, I was forced to limit the size of the training sequence I was using, so that the hidden Markov model would only bother trying to learn from the relevant data. Unfortunately, a training set of only 40 days is too small to work well. But 50 days is pushing it, and more than that is quite outdated any daily trading model.

The way around the problem was to use higher frequency data--because it would be relevant while still providing a wealth of information and hidden patterns. Besides all that, higher frequency data allows for more predictions to be made in any given day, and thus limits volatility in portfolio returns. (Real time prices are available through professional brokerage or subscriptions to specific Reuters or Yahoo Finance services. Delayed, but regularly updated prices are available on Google Finance, and no subscription is necessary.)

In order for a hidden Markov model--or any statistical strategy--to work, the trading techniques must be used many, many times. As the number of times the strategy is used increases, the variability in strategy's overall success decreases, and the strategy has more potential for a clean statistical edge to shine through. Conversely, if only a few instruments are held as a portfolio, the portfolio's return is less certain. Trading a few instruments with a prediction algorithm is like going spearfishing with a toothpick. It really is that impractical.

Also, if you know how to do something with a synthetic time series, do it. There tends to be much less variability in outcomes when unwanted risk factors are hedged, and thus much less uncertainty regarding the hidden Markov model's predictive ability.