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Lasso Inference for High-Dimensional Time Series

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  • Robert Adamek
  • Stephan Smeekes
  • Ines Wilms

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.

Suggested Citation

  • Robert Adamek & Stephan Smeekes & Ines Wilms, 2020. "Lasso Inference for High-Dimensional Time Series," Papers 2007.10952, arXiv.org, revised Sep 2022.
  • Handle: RePEc:arx:papers:2007.10952
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    Cited by:

    1. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    2. Robert Adamek & Stephan Smeekes & Ines Wilms, 2023. "Sparse High-Dimensional Vector Autoregressive Bootstrap," Papers 2302.01233, arXiv.org.
    3. Sander Barendse, 2023. "Expected Shortfall LASSO," Papers 2307.01033, arXiv.org, revised Jan 2024.
    4. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Inference in Non-stationary High-Dimensional VARs," Papers 2302.01434, arXiv.org, revised Sep 2023.
    5. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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