Predictable Latent Features Learning for High-Dimensional Seasonal Time Series Analysis and Forecasting

Analysis and prediction of high-dimensional time series are prevalent in numerous real-world scenarios, such as urban traffic. Traditional methods often struggle with the redundancy and cross-correlation inherent in such data, leading to computational inefficiencies and reduced accuracy. Additionally, the failure to account for seasonal characteristics further hampers their ability to capture essential temporal dependencies, thereby diminishing predictive accuracy. In this paper, we introduce a novel reduced-dimensional seasonal autoregressive modeling algorithm with a canonical correlation analysis objective (RDSAR-CCA) to simultaneously extract predictable latent features (PLFs) and forecast the future values of high-dimensional time series with seasonality. This algorithm first maps the original, high-dimensional time series into a latent, reduced-dimensional subspace, which simplifies the complex data into more easily analyzed and visualized forms. For each latent feature, an explicit seasonal autoregressive model is constructed to capture complex temporal dependencies. Further, a canonical correlation analysis-based objective is proposed to extract these PLFs one after another, with a descending order of predictability. The established explicit latent seasonal autoregressive models facilitate the prediction of PLFs and, consequently, enable the accurate prediction of the original data via inverse mapping. The effectiveness and superiority of the proposed algorithm are evaluated on a simulation example and the passenger flow data collected from 166 stations of the Shenzhen metro.