  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.
