Some Results on ℓ 1 Polynomial Trend Filtering

Hiroshi Yamada and Ruixue Du
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Hiroshi Yamada: Graduate School of Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan
Ruixue Du: Graduate School of Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan

Econometrics, 2018, vol. 6, issue 3, 1-10

Abstract: ℓ 1 polynomial trend filtering, which is a filtering method described as an ℓ 1 -norm penalized least-squares problem, is promising because it enables the estimation of a piecewise polynomial trend in a univariate economic time series without prespecifying the number and location of knots. This paper shows some theoretical results on the filtering, one of which is that a small modification of the filtering provides not only identical trend estimates as the filtering but also extrapolations of the trend beyond both sample limits.

Keywords: ℓ1 trend filtering; Hodrick–Prescott filtering; Whittaker–Henderson method of graduation; Lasso regression; basis pursuit denoising; total variation denoising (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2018
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