A simplified approach to parameter estimation and selection of sparse, mean reverting portfolios

In this paper, we study the problem of finding sparse, mean reverting portfolios in multivariate time series. This can be applied to developing profitable convergence trading strategies by identifying portfolios which can be traded advantageously when their prices differ from their identified long-term mean. Assuming that the underlying assets follow a VAR(1) process, we propose simplified, dense parameter estimation techniques which also provide a goodness of model fit measure based on historical data. Using these dense estimated parameters, we describe an exhaustive method to select an optimal sparse mean-reverting portfolio which can be used as a benchmark to evaluate faster, heuristic methods such as greedy search. We also present a simple and very fast heuristic to solve the same problem, based on eigenvector truncation. We observe that convergence trading using these portfolio selection methods is able to generate profits on historical financial time series.