# 1 Trend Filtering

@article{Kim20091TF, title={1 Trend Filtering}, author={Seung-Jean Kim and Kwangmoo Koh and Stephen P. Boyd and Dimitry M. Gorinevsky}, journal={SIAM Rev.}, year={2009}, volume={51}, pages={339-360} }

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed $\ell_1$ trend filtering method substitutes a sum of absolute values (i.e., $\ell_1$ norm) for the sum of squares used in H-P filtering to penalize variations in the estimated trend. The $\ell_1$ trend filtering method produces trend estimates that are piecewise linear… Expand

#### 435 Citations

HP Trend Filtering Using Gaussian Mixture Model Weighted Heuristic

- Mathematics, Computer Science
- 2014 IEEE 26th International Conference on Tools with Artificial Intelligence
- 2014

A modified version of HP weighted heuristic is presented that provides the best trend according to the abovementioned criteria and Gaussian Mixture Models on the preliminary estimated trend are used in the weighted HP heuristic to decrease the penalty in the objective function for turning-point intervals. Expand

Adaptive piecewise polynomial estimation via trend filtering

- Mathematics
- 2014

We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized… Expand

Trend Filtering: Empirical Mode Decompositions versus ℓ1 and Hodrick-Prescott

- Computer Science
- Adv. Data Sci. Adapt. Anal.
- 2011

This work proposes a novel approach based on empirical mode decomposition (EMD), called EMD trend filtering, which offers the possibility of estimating a trend of arbitrary shape as a sum of low-frequency intrinsic mode functions produced by the EMD. Expand

Business Cycles, Trend Elimination, and the HP Filter

- Mathematics
- 2015

We analyze trend elimination methods and business cycle estimation by data filtering of the type introduced by Whittaker (1923) and popularized in economics in a particular form by Hodrick and… Expand

$$\ell _{1}$$ Common Trend Filtering

- 2021

The $$\ell _{1}$$
trend filtering enables us to estimate a continuous piecewise linear trend of univariate time series. This filter and its variants have subsequently been applied in various fields,… Expand

Accurate Changing Point Detection for ℓ1 Mean Filtering

- Computer Science
- IEEE Signal Process. Lett.
- 2016

The main contribution in this paper is incorporating a technique to remove false changing points to a fast mean filtering algorithm, referred to as the taut-string method, resulting in an efficient procedure with accurate change point detection and thus the removal of the stair-case effect. Expand

Enhancements of Moving Trend Based Filters Aimed at Time Series Prediction

- Computer Science
- ICSS
- 2013

MTFs properties in frequency domain are considered, from seasonal time series decomposition, smoothing and prediction efficiency perspectives, and a number of MTFs enhancements is proposed, involving different approximating polynomials and final section signal corrections. Expand

Accurate Changing Point Detection for ${\ell _1}$ Mean Filtering

- IEEE Signal Processing Letters
- 2016

It is often desirable to find the underlying trends in time series data. This is a well known signal processing problem that has many applications in areas such as financial data analysis,… Expand

Wasserstein total variation filtering

- Engineering, Computer Science
- ArXiv
- 2019

A globally optimal algorithm for efficiently estimating the filtered signal under a Wasserstein finite differences operator is introduced and the efficacy of the proposed algorithm in preserving spatiotemporal trends in time series video is demonstrated in both simulated and fluorescent microscopy videos. Expand

Trend Filtering Methods for Momentum Strategies

- Engineering
- 2011

This paper studies trend filtering methods. These methods are widely used in momentum strategies, which correspond to an investment style based only on the history of past prices. For example, the… Expand

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