Learning Seasonal-Trend Representations and Conditional Heteroskedasticity for Time Series Analysis

Modeling and applying non-stationary time series with seasonal and trend features is a significant issue in the analysis of time series data. However, existing statistical methods decompose the series into seasonal and trend components, and ignore the correlation and conditional heteroskedasticity in residuals. In this paper, we present the first attempt to engage the autoregressive conditional heteroskedasticity (ARCH) in joint contemplation regarding the seasonal-trend decomposition, and extend the scope of learning seasonal-trend representations. We propose a novel model to learn seasonal-trend and conditional heteroskedasticity (STCH). We focus on understanding seasonal and trend patterns in data while also considering conditional heteroskedasticity, which is an important aspect in time series analysis. To be specific, we broaden the scope of the time series investigation by (1) simultaneously decomposing seasonal and trend components, (2) accounting for the correlation in the residuals, and (3) exploring the conditional heteroskedasticity within the residuals. Experiments on various numerical simulated data and real-world datasets have validated the accuracy and effectiveness of the proposed model and method.