English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we study the estimation of changing trends in time-series using$\ell_1$ trend filtering. This method generalizes 1D Total Variation (TV)denoising for detection of step changes in means to detecting changes intrends, and it relies on a convex optimization problem for which there are veryefficient numerical algorithms. It is known that TV denoising suffers from theso-called stair-case effect, which leads to detecting false change points. Theobjective of this paper is to show that $\ell_1$ trend filtering also suffersfrom a certain stair-case problem. The analysis is based on an interpretationof the dual variables of the optimization problem in the method as integratedrandom walk. We discuss consistency conditions for $\ell_1$ trend filtering,how to monitor their fulfillment, and how to modify the algorithm to avoid thestair-case false detection problem.

How to monitor and mitigate stair-casing in l1 trend filtering