Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many seasonal-trend decomposition algorithms suffer from high computational cost and require a large amount of data when multiple seasonal components exist, especially when the periodic length is long. In this paper, we propose a general and efficient multi-scale seasonal-trend decomposition algorithm for time series with multiple seasonality. We first down-sample the original time series onto a lower resolution, and then convert it to a time series with single seasonality. Thus, existing seasonal-trend decomposition algorithms can be applied directly to obtain the rough estimates of trend and the seasonal component corresponding to the longer periodic length. By considering the relationship between different resolutions, we formulate the recovery of different components on the high resolution as an optimization problem, which is solved efficiently by our alternative direction multiplier method (ADMM) based algorithm. Our experimental results demonstrate the accurate decomposition results with significantly improved efficiency.
翻译:许多实际世界时间序列显示多种季节性和不同长度的多重季节性。季节性成分的移走对于包括预测和异常检测在内的许多时间序列应用至关重要。然而,许多季节性趋势分解算法的计算成本很高,而且当存在多个季节性成分时需要大量数据,特别是当周期长度较长时。在本文件中,我们建议对具有多个季节性的时间序列采用普遍和高效的多尺度季节性分解算法。我们首先将原时间序列降为较低分辨率,然后将其转换为具有单一季节性的时间序列。因此,现有的季节性趋势分解算法可以直接用于获取趋势的粗估值和与较长周期长度相对应的季节性成分。我们通过考虑不同分辨率之间的关系,将高分辨率不同组成部分的回收编成一个优化问题,通过我们基于其他方向的乘数法(ADMM)的算法(AMM)有效解决。我们的实验结果显示准确的分解结果,并大大提高了效率。