An Improved Online Penalty Parameter Selection Procedure for $\ell_1$-Penalized Autoregressive with Exogenous Variables
This work addresses computational inefficiency in time series modeling for econometrics and related fields, though it appears incremental as it enhances an existing canonical model.
The authors tackled the problem of selecting penalty parameters for lasso-regularized autoregressive models with exogenous variables, proposing an online procedure that improved computational performance by 40% and forecast accuracy by 15% compared to existing methods in simulations and macroeconomic applications.
Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to regularize and provide feature selection. The lasso requires the specification of a penalty parameter that determines the degree of sparsity to impose. The most popular penalty parameter selection approaches that respect time dependence are very computationally intensive and are not appropriate for modeling certain classes of time series. We propose enhancing a canonical time series model, the autoregressive model with exogenous variables, with a novel online penalty parameter selection procedure that takes advantage of the sequential nature of time series data to improve both computational performance and forecast accuracy relative to existing methods in both a simulation and empirical application involving macroeconomic indicators.