Subset selection for vector autoregressive processes using Lasso

A subset selection method is proposed for vector autoregressive (VAR) processes using the Lasso [Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58, 267-288] technique. Simply speaking, Lasso is a shrinkage method in a regression setup which selects the model and estimates the parameters simultaneously. Compared to the conventional information-based methods such as AIC and BIC, the Lasso approach avoids computationally intensive and exhaustive search. On the other hand, compared to the existing subset selection methods with parameter constraints such as the top-down and bottom-up strategies, the Lasso method is computationally efficient and its result is robust to the order of series included in the autoregressive model. We derive the asymptotic theorem for the Lasso estimator under VAR processes. Simulation results demonstrate that the Lasso method performs better than several conventional subset selection methods for small samples in terms of prediction mean squared errors and estimation errors under various settings. The methodology is applied to modeling U.S. macroeconomic data for illustration.