In finance, statistical arbitrage refers to automated trading strategies that are typical of a short-term and involve a large number of securities.
In such strategies, the user tries to implement a trading algorithm for a set of securities on the basis of quantities such as historical correlations and general economic variables. These measurements can be cast as a classification or estimation problem. The basic assumption is that prices will move towards a historical average.
We apply machine learning methods to obtain an index arbitrage strategy. In particular, we employ linear regression and support vector regression (SVR) onto the prices of an exchange-traded fund and a stream of stocks.
By using principal component analysis (PCA) in reducing the dimension of feature space, we observe the benefit and note the issues in the application of SVR.
To generate trading signals, we model the residuals from the previous regression as a mean-reverting process. In the case of classification, the categories might be sold, buy or do nothing for each security.
Also one might try to predict the expected return of each security over a future time horizon.
In this case, one typically needs to use the estimates of the expected return to make a trading decision(buy, sell, etc.)