MDL-Based Analysis of Time Series at Multiple Time-Scales

The behavior of many complex physical systems is affected by a variety of phenomena occurring at different temporal scales. Time series data produced by measuring properties of such systems often mirrors this fact by appearing as a composition of signals across different time scales. When the final goal of the analysis is to model the individual phenomena affecting a system, it is crucial to be able to recognize the right temporal scales and to separate the individual components of the data. In this paper, we approach this challenge through a combination of the Minimum Description Length (MDL) principle, feature selection strategies, and convolution techniques from the signal processing field. As a result, our algorithm produces a good decomposition of a given time series and, as a side effect, builds a compact representation of its identified components. Experiments demonstrate that our method manages to identify correctly both the number and the temporal scale of the components for real-world as well as artificial data and show the usefulness of our method as an exploratory tool for analyzing time series data.