Elastic trend filtering

Abstract

Abstract Trend filtering aims to estimate underlying trends in time series data, which is necessary to investigate data in a variety of disciplines. We propose a new method called elastic trend filtering. The proposed method combines ℓ 2 and ℓ 1 norm penalties to exploit the benefits and strengths of Hodrick–Prescott and ℓ 1 trend filterings. We apply the alternating direction method of multipliers for its efficient computation and numerical experiments show the soundness and efficiency of the proposed method. We further apply the proposed method to graph cases for potential applications and suggest a trend filtering for its variance estimate.