  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.
