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.

翻译：周期检测是时间序列分析中的重要任务，但由于时间序列数据具有突变趋势、离群值、噪声以及尤其严重的块状缺失数据等多样特征，该问题仍具挑战性。本文针对含块状缺失数据的时间序列，提出一种鲁棒且高效的周期检测算法。首先，我们设计了一种鲁棒的趋势滤波器，以消除缺失数据下复杂趋势模式带来的干扰。其次，提出一种能够有效处理缺失值和离群值的鲁棒自相关函数，并严格证明：当缺失块长度小于周期长度的三分之一时，该鲁棒自相关函数仍能有效工作。最后，通过结合时频信息，算法可精准生成周期长度。实验结果表明，该算法在真实时间序列数据集上的性能优于现有周期检测算法。