Modeling Latent Patterns in Time Series Residuals for Forecasting Purposes

Abstract

This article investigates the problem of improving the accuracy of time series forecasting by identifying and modeling hidden structural patterns in their residual components. Time series, representing sequences of observations, play a crucial role in data analysis across various applied domains. However, their forecasting is often complicated by the presence of complex nonlinear dependencies. Traditionally, the residual component obtained after series decomposition is interpreted as random noise lacking predictive value. The first part of the article provides a detailed review of modern approaches, highlighting the growing trend of rethinking this paradigm and focusing on extracting useful signals from residuals. The second part of the article pays special attention to two advanced hybrid deep learning architectures: CNN-GRU and Transformer-GRU. These methods represent modern tools that combine the analysis of local spatial patterns and global temporal dependencies to model complex structures in residuals. Experimental research conducted on real-world data from retail sales, social statistics, and financial series confirmed the presence of structural patterns in residual components and established that the effectiveness of hybrid architectures is determined by the nature of the data. This article aims to contribute to the development of time series analysis methods by providing a tool for extracting additional information, which directly impacts the quality of forecast construction.