This paper generalizes the univariate results of Chan and Tran (1989, <italic>Econometric Theory</italic> 5, 354–362) and Phillips (1990, <italic>Econometric Theory</italic> 6, 44–62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and...

This paper proposes the least absolute shrinkage and selection operator–type (Lasso-type) generalized method of moments (GMM) estimator. This Lasso-type estimator is formed by the GMM objective function with the addition of a penalty term. The exponent of the penalty term in the regular Lasso...