Bias-reduced ℓ1-trend filtering
Donghyeon Yu, Johan Lim, Won Jun Son · Communications for Statistical Applications and Methods · 2023
The ℓ 1 -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 ℓ 1 -trend filtering gives piecewise linear trends.One of the advantages of the ℓ 1 -trend filtering is that it can be used for identifying change points in piecewise linear trends.However, since the ℓ 1 -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 ℓ 1 -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 ℓ 1 -trend filtering.Numerical examples illustrate that the proposed method yields less biased estimates for piecewise linear trends.