Periodicity detection is a crucial step in time series tasks, including monitoring and forecasting of metrics in many areas, such as IoT applications and self-driving database management system. In many of these applications, multiple periodic components exist and are often interlaced with each other. Such dynamic and complicated periodic patterns make the accurate periodicity detection difficult. In addition, other components in the time series, such as trend, outliers and noises, also pose additional challenges for accurate periodicity detection. In this paper, we propose a robust and general framework for multiple periodicity detection. Our algorithm applies maximal overlap discrete wavelet transform to transform the time series into multiple temporal-frequency scales such that different periodic components can be isolated. We rank them by wavelet variance, and then at each scale detect single periodicity by our proposed Huber-periodogram and Huber-ACF robustly. We rigorously prove the theoretical properties of Huber-periodogram and justify the use of Fisher's test on Huber-periodogram for periodicity detection. To further refine the detected periods, we compute unbiased autocorrelation function based on Wiener-Khinchin theorem from Huber-periodogram for improved robustness and efficiency. Experiments on synthetic and real-world datasets show that our algorithm outperforms other popular ones for both single and multiple periodicity detection.

翻译：周期性检测是时间序列任务中的一个关键步骤,包括监测和预报许多领域(如IoT应用程序和自我驱动数据库管理系统等)的测量数据。在许多这些应用中,存在多个周期性组件,而且往往相互交织。这种动态和复杂的周期性模式使得准确周期性检测很困难。此外,时间序列中的其他组件,如趋势、异常值和噪音,也给准确周期检测带来额外挑战。在本文件中,我们提议一个可靠和一般的多周期检测框架。我们的算法应用最大重叠离散波盘转换,将时间序列转换成多个时频尺度,这样可以隔开不同的周期性组件。我们用波质差异进行分级,然后在每个尺度上用我们拟议的Huber-周期图和Huber-ACF 有力地检测单一周期周期性模式来检测它们。我们严格地证明Huber- 周期图的理论性属性,并证明使用Fishercher的测试进行周期性检测的合理性。为了进一步完善检测周期性周期性,我们根据Wen-Khinchine-sin 周期性分类转换成不同的周期性比例尺度,我们用一个周期性模型来测量系统系统显示我们真实和超时空的系统测试中的数据。