# statistical arbitrage using PCA

While reading the paper Statistical Arbitrage in the U.S. Equities Market by Marco Avellaneda and Jeong-Hyun Lee on statistical arbitrage using PCA

I realized that the author sums the residuals of regression against PCA factors and says that is mean reverting. By standard regression principles aren't residuals IID normal and hence their sum should be a random walk? Then how can the sum of residuals be mean reverting?

## 1 Answer

The estimation of the parameters by regression ensures that the mean of the residuals is 0. So, technically the residuals are not IID as if the number of observations is $$n$$, any $$n-1$$ residuals completely determine the last one.

In practice, the assumption of iid-ness is not realistic anyway.