The Doubly Adaptive LASSO for Vector Autoregressive Models

The LASSO (Tibshirani, J R Stat Soc Ser B 58(1):267-288, 1996, [30]) and the adaptive LASSO (Zou, J Am Stat Assoc 101:1418-1429, 2006, [37]) are popular in regression analysis for their advantage of simultaneous variable selection and parameter estimation, and also have been applied to autoregressive time series models. We propose the doubly adaptive LASSO (daLASSO), or PLAC-weighted adaptive LASSO, for modelling stationary vector autoregressive processes. The procedure is doubly adaptive in the sense that its adaptive weights are formulated as functions of the norms of the partial lag autocorrelation matrix function (Heyse, 1985, [17]) and Yule-Walker or ordinary least squares estimates of a vector time series. The existing papers ignore the partial lag autocorrelation information inherent in a VAR process. The procedure shows promising results for VAR models. The procedure excels in terms of VAR lag order identification.