A Theory-based Lasso for Time-Series Data

Achim Ahrens, Christopher Aitken, Jan Ditzen, Erkal Ersoy, David Kohns, Mark Edwin Schaffer

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Abstract

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 vs. 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).
Original languageEnglish
JournalStudies in Computational Intelligence
Publication statusAccepted/In press - 8 Jan 2020
Event3rd International Econometric Conference of Vietnam 2020: Data Science for Financial Econometrics - Banking University of Ho-Chi-Minh City, Ho-Chi-Minh City, Viet Nam
Duration: 14 Jan 202016 Jan 2020
http://hcm-hn.conference-econ-buh-bav-rist.vn/trang-chu.html

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Keywords

  • Lasso
  • Machine learning
  • Time-series
  • Dependence

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