Lasso Inference for High-Dimensional Time Series

Robert Adamek, Stephan Smeekes and Ines Wilms

Papers from arXiv.org

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.

Date: 2020-07, Revised 2022-09
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Journal Article: Lasso inference for high-dimensional time series (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2007.10952

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