ForeCA: Forecastable Component Analysis

Abstract: Blind source separation (BSS) techniques are often applied to multivariate time series with the goal to obtain better forecasts. But BSS and the need for better forecasts are often treated separately, in the sense that finding an optimally transformed (sub-)space has nothing to do with the aim to predict well. Here I introduce Forecastable Component Analysis (ForeCA), a new BSS technique for temporally dependent signals that uses forecastability as the explicit objective in finding an optimal transformation. It separates the signal into the forecastable, $\mathbf{F}$, and the orthogonal white noise space, $\mathbf{F}^{\bot}$. Simulations and applications to financial data show that ForeCA successfully finds signals that can be used to forecast. ForeCA therefore automatically discovers informative structure in multivariate signals. The R package (http://cran.r-project.org/web/packages/ForeCA/index.html) will be publicly available on CRAN upon publication of the manuscript.