Sequential Decomposition of Multiple Seasonal Components Using Spectrum-Regularized Periodic Gaussian Process

Abstract

Many real-world time series, such as electricity demand data, biomedical signals, and mechanical vibration signals, exhibit complex trends, encompass multiple seasonal (or periodic) components, and are prone to noise contamination. Existing decomposition methods encounter difficulties when confronted with unknown periods and the presence of multiple nonlinear seasonal components. To address these challenges, we propose a novel nonparametric approach based on periodic Gaussian process models, called sequential seasonal-trend decomposition (SSTD). This model is capable of extracting multiple seasonal components sequentially while estimating the component periods. A spectrum-regularized periodic Gaussian process is proposed to sequentially extract each of the seasonal components, leveraging Fourier basis functions to represent the remaining components. The unknown periods are estimated through a tailored two-step parameter estimation technique from the non-convex likelihood. To mitigate the computational complexity of the proposed method, we propose a circulant acceleration approach. By enabling the sequential extraction of multiple seasonal components and the estimation of unknown periods, SSTD bridges a gap in existing methodologies, yielding improved accuracy and efficiency. Empirical studies on synthetic and real-world data demonstrate its outperformance over current methods.