Periodic Measures and Wasserstein Distance for Analysing Periodicity of Time Series Datasets
发布时间：2023年04月03日
浏览次数：2649
发布者: He Liu
主讲人： 赵怀忠（杜伦大学，山东大学）
活动时间： 从 2023-04-10 14:00 到 15:00
场地： 理科一号楼 1114教室
In this talk, I will talk about the results in a new paper, jointly written with Chunrong Feng and Yujia Liu, mainly on the probability foundation of the periodic measure approach inanalysing periodicity of a dataset. It is based on recent work of random periodic processes. While random periodic paths provide a pathwise model for time series datasets with a periodic pattern, their law is a periodic measure and gives a statistical description and the ergodic theory offers a scope of statistical analysis. The connection of a sample path and the periodic measure is revealed in the law of large numbers (LLN). We prove first the period is actually a deterministic number and then for discrete processes, {B\'{e}zout's identity comes in naturally in the LLN along an arithmetic sequence of an arbitrary increment.} The limit is a periodic measure whose period is equal to the greatest common divisor between the test period and the true period of the random periodic process. This leads to a new scheme of detecting random periodicity of a dataset and finding its period, as an alternative to the Discrete Fourier Transformation (DFT) and periodogram approach. We find that in some situations, the classical method does not work robustly, but the new one can work efficiently. We prove that the periodicity is quantified by the Wasserstein distance, in which the convergence of empirical distributions is established.
