Enhancing Multivariate Time Series Prediction: The UVARX Model for CO2 Emissions and Economic Growth

Multivariate time series analysis is a crucial tool for examining the interdependence of multiple variables over time. Traditional probabilistic models require precise observational data. However, in practical applications, some variables are subject to inherent uncertainties that cannot be accurately quantified. To address this limitation, this paper introduces an uncertain vector autoregressive model with exogenous variables (UVARX) to incorporate uncertainty into multivariate time series analysis. The proposed model distinguishes between endogenous and exogenous variables, leveraging uncertainty theory to accommodate imprecise observations. A rigorous statistical framework — encompassing parameter estimation, residual analysis, uncertain hypothesis test, cross-validation, and predictive evaluation — is employed to validate the model. Empirical analysis on the joint forecasting of [Formula: see text] emissions and GDP, with electricity consumption as an exogenous factor, demonstrates the model’s capability to handle imprecise data effectively. Results indicate that the UVARX model outperforms conventional approaches in forecasting accuracy, providing a robust analytical tool for uncertain multivariate time series. Since the transportation sector, particularly the automotive industry, is a major contributor to global [Formula: see text] emissions, the proposed methodology demonstrates strong potential for applications in intelligent vehicle systems and AI-driven energy management.