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In statistical arbitrage with PCA factors on returns, do historical returns path matter?

Paper: https://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf

One thing I am a bit confused is that although many cointegration techniques rely on long term relationships among stocks, pca factors approach seem to look at the relationships based on a point in time returns?

For example, in this paper, although model estimation and building pca factors use historical data, to see if a next period residuals is above or below standard deviation threshold, doesn't it simply fit the factors based on loadings and one period returns? So even if one stock has been constantly outperforming the other ones, it would not consider that historical returns.

1 response

PCA (Principal Component Analysis) uses historical data to determine the most predictive Principal Components for forecasting asset returns.
It is an approach to find those components that provide the best statistical explanation of prior returns and use those factors to forecast future returns.
Once you have selected your components they are not evaluated again, unless you redo your PCA analysis.
The idea being that If your components have good predictive power, then you shouldn't change your components, any short term deviations are due to noise and you should stick with the long-term predictors.

If you redo the PCA all the time then you are just calibrating the model over and over, constantly changing what you believe drives returns and chasing noise.

I've only used it in the HJM interest rate model to determine which tenors are the best predictors of future interest rates.
Thanks for sharing the link to the paper.

Best