Periodic measures and Wasserstein distance for analysing periodicity of time series datasets

In this article, we establish the probability foundation of periodic measure approach in analysing periodicity a dataset. It is based on recent work random processes. While paths provide pathwise model for time series datasets with pattern, their law and gives statistical description ergodic theory offers scope analysis. The connection sample path revealed large numbers (LLN). We prove first period actually deterministic number then discrete processes, Bézout’s identity comes naturally LLN along an arithmetic sequence arbitrary increment. limit whose equal to greatest common divisor between test true process. This leads new scheme detecting dataset finding its period, as alternative Discrete Fourier Transformation (DFT) periodogram approach. find that some situations, classical method does not robustly, but one can efficiently. quantified by Wasserstein distance, which convergence empirical distributions established.