Liang Sun

Qingsong Wen, Linxiao Yang, Liang Sun

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.

Tian Zhou, Ziqing Ma, Qingsong Wen et al.

Although Transformer-based methods have significantly improved state-of-the-art results for long-term series forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series (e.g. overall trend). To address these problems, we propose to combine Transformer with the seasonal-trend decomposition method, in which the decomposition method captures the global profile of time series while Transformers capture more detailed structures. To further enhance the performance of Transformer for long-term prediction, we exploit the fact that most time series tend to have a sparse representation in well-known basis such as Fourier transform, and develop a frequency enhanced Transformer. Besides being more effective, the proposed method, termed as Frequency Enhanced Decomposed Transformer ({\bf FEDformer}), is more efficient than standard Transformer with a linear complexity to the sequence length. Our empirical studies with six benchmark datasets show that compared with state-of-the-art methods, FEDformer can reduce prediction error by $14.8\%$ and $22.6\%$ for multivariate and univariate time series, respectively. Code is publicly available at https://github.com/MAZiqing/FEDformer.