Scale Invariant and Robust Pattern Identification in Univariate Time Series, with Application to Growth Trend Detection in Music Streaming Data

Abstract

A method is proposed to identify a pre-defined pattern in univariate time series. The pattern could describe an expected trend, for example, the development of a “hit” in music streaming data, with a rapid increase of the number of streams, to a peak, and a slow decay. With this application in mind, the method is scale invariant in the time domain as well as for the values of the time series (e.g., number of streams). Moreover, it is suitable also for irregularly spaced time series, and robust against short-term seasonal movements, as well as to noisy and spiky time series. Simulation studies compare this proposal with a method for identifying breaks in a time series. If the number of breaks for this method is pre-defined, the windows with the simulated patterns can be well identified with both procedures. The new proposal can additionally filter out those time series which contain the pre-defined pattern. This method is applied to a big data base of digital music streaming data for the purpose of “hit” detection.