Regularized Robust Portfolio Estimation

We study the problem of learning a combination (e.g. a portfolio) of time series that has large autocorrelation. This is a challenging task as it involves the lag-1 autocovariance matrix of the series, which is difficult to estimate in practice. To address this issue we develop regularized versions of the autocorrelation function based on a robust optimization formulation of the problem. We highlight different forms of regularizers and present a method to solve the underlying optimization problem. We also discuss an extension of our approach to find maximally crosscorrelated combinations of time series, which provides a novel class of regularization techniques for canonical correlation analysis. Experiments in the context of financial time series, where the estimation of the lag-1 autocovariance matrix is notoriously difficult, indicate the potential of the proposed approach.