Robust-STP: A Robust Seasonal-trend Decomposition Method for Partial Periodic Time Series

Abstract

The extraction of trend and seasonal components from time series is essential for tasks such as forecasting and anomaly detection of the data. The existing decomposition methods of time series mainly concentrate on full-period time series, that is, the periodicity of data runs through the whole time series, less effort has been paid on those kinds of time series that with the mixture of periodicity and aperiodicity. However, in the real world, much of the time series appears mostly in a mixture of periodicity and aperiodicity. Based on this consideration, in this paper, we propose a novel robust seasonal-trend decomposition method for partially periodic time series, short for Robust-STP, to fill this research gap. Firstly, we use bilateral filtering and least absolute deviation loss with regularizations to remove noise and relative trends in the data. Secondly, a sliding window based on the dynamic time warping algorithm is employed to locate the interval points between periodic and aperiodic data. Finally, seasonal and trend filters are imposed to extract the final seasonal and trend components, respectively. Experimental results on synthetic and real datasets are proved to the effectiveness of Robust-STP on partial periodic time series.