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Statistical optimality benchmarking is crucial for analyzing and designingtime series classification (TSC) algorithms. This study proposes to benchmarkthe optimality of TSC algorithms in distinguishing diffusion processes by thelikelihood ratio test (LRT). The LRT is an optimal classifier by theNeyman-Pearson lemma. The LRT benchmarks are computationally efficient becausethe LRT does not need training, and the diffusion processes can be efficientlysimulated and are flexible to reflect the specific features of real-worldapplications. We demonstrate the benchmarking with three widely-used TSCalgorithms: random forest, ResNet, and ROCKET. These algorithms can achieve theLRT optimality for univariate time series and multivariate Gaussian processes.However, these model-agnostic algorithms are suboptimal in classifyinghigh-dimensional nonlinear multivariate time series. Additionally, the LRTbenchmark provides tools to analyze the dependence of classification accuracyon the time length, dimension, temporal sampling frequency, and randomness ofthe time series.

Benchmarking optimality of time series classification methods in distinguishing diffusions