Time-varying Lasso

This paper introduces a Lasso-type estimator for large linear models with time-varying parameters. The estimator is easy to implement in practice and standard algorithms developed for Lasso with fixed parameters can be readily used. We derive theoretical properties of the estimator, allowing for deterministic or stochastic smoothly varying parameter processes and discuss ways in which tuning parameters can be data dependent. Monte Carlo simulation and an application to forecasting inflation with macroeconomic variables illustrates the usefulness of our method.