Lasso Inference for High-Dimensional Time Series

TL;DR

This paper develops a method for valid statistical inference in high-dimensional time series using an extended desparsified lasso approach that accounts for serial dependence, heteroskedasticity, and non-Gaussianity.

Contribution

It extends the desparsified lasso to high-dimensional, dependent, and heteroskedastic time series under NED assumptions, providing asymptotic normality and variance estimation tools.

Findings

The method achieves accurate inference in simulations.

It handles non-Gaussian, serially correlated, heteroskedastic processes.

The approach works even when the number of regressors grows faster than the sample size.

Abstract

In this paper we develop valid inference for high-dimensional time series. We extend the desparsified lasso to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an error bound under weak sparsity, which, coupled with the NED assumption, means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the desparsified lasso. This allows us to establish the uniform asymptotic normality of the desparsified lasso under general conditions, including for inference on parameters of increasing dimensions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear time series models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the desparsified lasso in common time series settings.