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Many recent developments in the high-dimensional statistical time seriesliterature have centered around time-dependent applications that can be adaptedto regularized least squares. Of particular interest is the lasso, which bothserves to regularize and provide feature selection. The lasso requires thespecification of a penalty parameter that determines the degree of sparsity toimpose. The most popular penalty parameter selection approaches that respecttime dependence are very computationally intensive and are not appropriate formodeling certain classes of time series. We propose enhancing a canonical timeseries model, the autoregressive model with exogenous variables, with a novelonline penalty parameter selection procedure that takes advantage of thesequential nature of time series data to improve both computational performanceand forecast accuracy relative to existing methods in both a simulation andempirical application involving macroeconomic indicators.

An Improved Online Penalty Parameter Selection Procedure for $\ell_1$-Penalized Autoregressive with Exogenous Variables