A Formally Robust Time Series Distance Metric

Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various different distance metrics or measures dedicated to particular aspects of real-world time series data, yet there is an important aspect that has not been considered so far: Robustness against arbitrary data contamination. In this work, we propose a novel distance metric that is robust against arbitrarily "bad" contamination and has a worst-case computational complexity of $\mathcal{O}(n\log n)$. We formally argue why our proposed metric is robust, and demonstrate in an empirical evaluation that the metric yields competitive classification accuracy when applied in k-Nearest Neighbor time series classification.

Robust Parameter-Free Season Length Detection in Time Series

The in-depth analysis of time series has gained a lot of research interest in recent years, with the identification of periodic patterns being one important aspect. Many of the methods for identifying periodic patterns require time series' season length as input parameter. There exist only a few algorithms for automatic season length approximation. Many of these rely on simplifications such as data discretization and user defined parameters. This paper presents an algorithm for season length detection that is designed to be sufficiently reliable to be used in practical applications and does not require any input other than the time series to be analyzed. The algorithm estimates a time series' season length by interpolating, filtering and detrending the data. This is followed by analyzing the distances between zeros in the directly corresponding autocorrelation function. Our algorithm was tested against a comparable algorithm and outperformed it by passing 122 out of 165 tests, while the existing algorithm passed 83 tests. The robustness of our method can be jointly attributed to both the algorithmic approach and also to design decisions taken at the implementational level.