# RobustPeriod: Time-Frequency Mining for Robust Multiple Periodicity Detection

arXiv: https://arxiv.org/abs/2002.09535 · HTML: https://mlsanity.com/paper/2002.09535/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [AHPA: Adaptive Horizontal Pod Autoscaling Systems on Alibaba Cloud Container Service for Kubernetes](https://mlsanity.com/paper/2303.03640/) (2023)
- [Robust Time Series Dissimilarity Measure for Outlier Detection and Periodicity Detection](https://mlsanity.com/paper/2206.02956/) (2022)
- [A Joint Time-frequency Domain Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2305.14649/) (2023)
- [A Robust and Efficient Multi-Scale Seasonal-Trend Decomposition](https://mlsanity.com/paper/2109.08800/) (2021)
- [Robust Dominant Periodicity Detection for Time Series with Missing Data](https://mlsanity.com/paper/2303.03553/) (2023)
- [Two-Stage Framework for Seasonal Time Series Forecasting](https://mlsanity.com/paper/2103.02144/) (2021)
- [CEDAR: Controlled and Event-Driven Demand Forecasting via Residual Decomposition](https://mlsanity.com/paper/2608.25871/) (2026)

## Abstract (arXiv)

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.