# Robust Dominant Periodicity Detection for Time Series with Missing Data

arXiv: https://arxiv.org/abs/2303.03553 · HTML: https://mlsanity.com/paper/2303.03553/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [RobustTAD: Robust Time Series Anomaly Detection via Decomposition and Convolutional Neural Networks](https://mlsanity.com/paper/2002.09545/) (2020)
- [RobustSTL: A Robust Seasonal-Trend Decomposition Algorithm for Long Time Series](https://mlsanity.com/paper/1812.01767/) (2018)
- [TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis](https://mlsanity.com/paper/2210.09693/) (2022)
- [RobustTrend: A Huber Loss with a Combined First and Second Order Difference Regularization for Time Series Trend Filtering](https://mlsanity.com/paper/1906.03751/) (2019)
- [RobustPeriod: Time-Frequency Mining for Robust Multiple Periodicity Detection](https://mlsanity.com/paper/2002.09535/) (2020)
- [A Robust and Efficient Multi-Scale Seasonal-Trend Decomposition](https://mlsanity.com/paper/2109.08800/) (2021)
- [Two-Stage Framework for Seasonal Time Series Forecasting](https://mlsanity.com/paper/2103.02144/) (2021)

## Built on by (most cited first, 3 of 3)

- [An Unsupervised Approach for Periodic Source Detection in Time Series](https://mlsanity.com/paper/2406.00566/) (2024)
- [RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems](https://mlsanity.com/paper/2510.17396/) (2025)
- [T2M Mamba: Motion Periodicity-Saliency Coupling Approach for Stable Text-Driven Motion Generation](https://mlsanity.com/paper/2602.01352/) (2026)

## Abstract (arXiv)

Periodicity detection is an important task in time series analysis, but still a challenging problem due to the diverse characteristics of time series data like abrupt trend change, outlier, noise, and especially block missing data. In this paper, we propose a robust and effective periodicity detection algorithm for time series with block missing data. We first design a robust trend filter to remove the interference of complicated trend patterns under missing data. Then, we propose a robust autocorrelation function (ACF) that can handle missing values and outliers effectively. We rigorously prove that the proposed robust ACF can still work well when the length of the missing block is less than 1/3 of the period length. Last, by combining the time-frequency information, our algorithm can generate the period length accurately. The experimental results demonstrate that our algorithm outperforms existing periodicity detection algorithms on real-world time series datasets.