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Econometrics 2018, 6(3), 33; https://doi.org/10.3390/econometrics6030033

Some Results on 1 Polynomial Trend Filtering

Graduate School of Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan
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Received: 22 May 2018 / Revised: 30 June 2018 / Accepted: 4 July 2018 / Published: 10 July 2018
(This article belongs to the Special Issue Filtering)
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Abstract

1 polynomial trend filtering, which is a filtering method described as an 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. View Full-Text
Keywords: ℓ1 trend filtering; Hodrick–Prescott filtering; Whittaker–Henderson method of graduation; Lasso regression; basis pursuit denoising; total variation denoising ℓ1 trend filtering; Hodrick–Prescott filtering; Whittaker–Henderson method of graduation; Lasso regression; basis pursuit denoising; total variation denoising
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Yamada, H.; Du, R. Some Results on 1 Polynomial Trend Filtering. Econometrics 2018, 6, 33.

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