A Theory-based Lasso for Time-Series Data

We present two new lasso estimators, the HAC-lasso and AC-lasso, that are suitable for time-series applications. The estimators are variations of the theory-based or ‘rigorous’ lasso of Bickel et al. (2009), Belloni et al. (2011), Belloni and Chernozhukov (2013), Belloni et al. (2016) and recently extended to the case of dependent data by Chernozhukov et al. (2019), where the lasso penalty level is derived on theoretical grounds. The rigorous lasso has appealing theoretical properties and is computationally very attractive compared to conventional cross-validation. The AC-lasso version of the rigorous lasso accommodates dependence in the disturbance term of arbitrary form, so long as the dependence is known to die out after q periods; the HAC-lasso also allows for heteroskedasticity of arbitrary form. The HAC- and AC-lasso are particularly well-suited to applications such as nowcasting, where the time series may be short and the dimensionality of the predictors is high. We present some Monte Carlo comparisons of the performance of the HAC-lasso versus penalty selection by cross-validation approach. Finally, we use the HAC-lasso to estimate a nowcasting model of US GDP growth based on Google Trends data and compare its performance to the Bayesian methods employed by Kohns and Bhattacharjee (2019).