RobustPeriod: Time-Frequency Mining for Robust Multiple Periodicity Detection
This work addresses periodicity detection for applications like IoT and database management, offering a robust solution but is incremental as it builds on existing wavelet and robust statistical techniques.
The paper tackles the problem of detecting multiple periodic components in time series, which is challenging due to dynamic patterns and interference from trends and noise, by proposing a robust framework that uses wavelet transforms and Huber-based methods, achieving superior performance in experiments on synthetic and real-world datasets.
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.