A trend filtering method closely related to $$\ell _{1}$$ ℓ 1 trend filtering

Hiroshi Yamada ()
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Hiroshi Yamada: Hiroshima University

Empirical Economics, 2018, vol. 55, issue 4, No 2, 1413-1423

Abstract: Abstract The filtering method developed by Kim et al. (SIAM Rev 51:339–360, 2009), $$\ell _{1}$$ ℓ 1 trend filtering, is attractive because it enables us to estimate a continuous piecewise linear trend. This paper introduces a new filtering method closely related to $$\ell _{1}$$ ℓ 1 trend filtering in order to contribute to the accumulation of knowledge on $$\ell _{1}$$ ℓ 1 trend filtering. We show that the piecewise linearity, which is the key feature of $$\ell _{1}$$ ℓ 1 trend filtering, is derived from the new filtering. For this reason, we refer to the filtering as ‘pure’ $$\ell _{1}$$ ℓ 1 trend filtering. We also demonstrate some other miscellaneous results concerning the new filtering.

Keywords: $$\ell _{1}$$ ℓ 1 trend filtering; Generalized lasso regression; Hodrick–Prescott filtering; Ridge regression; Penalized least squares; 1d fused lasso; Total variation denoising (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00181-017-1349-8

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