Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering

Abstract

In this paper, we propose a nonparametric approach that can be used in envelope extraction, peak-burst detection and clustering in time series. Our problem formalization results in a naturally defined splitting/forking of the time series. With a possibly hierarchical implementation, it can be used for various applications in machine learning, signal processing and mathematical finance. From an incoming input signal, our iterative procedure sequentially creates two signals (one upper bounding and one lower bounding signal) by minimizing the cumulative $L_1$ drift. We show that a solution can be efficiently calculated by use of a Viterbi-like path tracking algorithm together with an optimal elimination rule. We consider many interesting settings, where our algorithm has near-linear time complexities.