Estimation and HAC-based Inference for Machine Learning Time Series Regressions

Time series regression analysis in econometrics typically involves a framework relying on a set of mixing conditions to establish consistency and asymptotic normality of parameter estimates and HAC-type estimators of the residual long-run variances to conduct proper inference. This article introduces structured machine learning regressions for high-dimensional time series data using the aforementioned commonly used setting. To recognize the time series data structures we rely on the sparse-group LASSO estimator. We derive a new Fuk-Nagaev inequality for a class of $\tau$-dependent processes with heavier than Gaussian tails, nesting $\alpha$-mixing processes as a special case, and establish estimation, prediction, and inferential properties, including convergence rates of the HAC estimator for the long-run variance based on LASSO residuals. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that the text data can be a useful addition to more traditional numerical data.