T3PRF: Three Pass Regression Filter for R

The Three Pass Regression Filter

Consider a linear regression model with a large number of predictors. If the number of predictors is close to the number of observations or greater then the OLS estimate is poorly behaved or inexistent. A typical solution would be to assume a latent factor structure. That is to say, one would assume that the predictors are explained by a limited number of latent factors.

Principal component regression (PCR), where the factors are some of the principal components of the predictors is an example of such an approach.

In the context of forecasting a criticism of PCR would that the extracted factors are not chosen with respect to target. The factors (principal components), are selected to minimize the reconstruction error but the correlation with the target is not considered.

By assuming that the same latent factors explain both the target and the predictors, The Three Pass Regression Filter(T3PRF) selects the components in such a way to minimize the reconstruction error while at same time maximizing the correlation with the target.

References:

Kelly, Bryan T. and Pruitt, Seth, The Three-Pass Regression Filter: A New Approach to Forecasting Using Many Predictors (May 2014). Fama-Miller Working Paper; Chicago Booth Research Paper No. 11-19. Available at SSRN: http://ssrn.com/abstract=1868703 or http://dx.doi.org/10.2139/ssrn.1868703

TODOS

Complete Documentation

Add asymptotics

Add examples

Add vignette

Improve testing

Improve handling of missing values

CANCELLED Move from RcppEigen to native .Call with LAPACK

Add GPU support especially for rolling and recursive forecasts