Lag weighted lasso for time series model

The adaptive lasso can consistently identify the true model in regression model. However, the adaptive lasso cannot account for lag effects, which are essential for a time series model. Consequently, the adaptive lasso can not reflect certain properties of a time series model. To improve the forecast accuracy of a time series model, we propose a lag weighted lasso. The lag weighted lasso imposes different penalties on each coefficient based on weights that reflect not only the coefficients size but also the lag effects. Simulation studies and a real example show that the proposed method is superior to both the lasso and the adaptive lasso in forecast accuracy.