Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Bias-reduced ℓ1-trend filtering

  • Donghyeon Yu (Department of Statistics, Inha University) ;
  • Johan Lim (Department of Statistics, Seoul National University) ;
  • Won Son (Department of Information Statistics, Dankook University)
  • Received : 2022.08.11
  • Accepted : 2022.12.26
  • Published : 2023.03.31
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Abstract

The ℓ1-trend filtering method is one of the most widely used methods for extracting underlying trends from noisy observations. Contrary to the Hodrick-Prescott filtering, the ℓ1-trend filtering gives piecewise linear trends. One of the advantages of the ℓ1-trend filtering is that it can be used for identifying change points in piecewise linear trends. However, since the ℓ1-trend filtering employs total variation as a penalty term, estimated piecewise linear trends tend to be biased. In this study, we demonstrate the biasedness of the ℓ1-trend filtering in trend level estimation and propose a two-stage bias-reduction procedure. The newly suggested estimator is based on the estimated change points of the ℓ1-trend filtering. Numerical examples illustrate that the proposed method yields less biased estimates for piecewise linear trends.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A5A7033499 (Donghyeon Yu), No. 2021R1A2C1 010786 (Johan Lim), and No. 2020R1F1A1A01051039 (Won Son)).

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