Research Article

Nonlinear Nonparametric Uncertain Autoregressive Time Series Model

Abstract

Uncertain time series analysis provides a framework for modeling data shaped by human belief and cognitive limitations rather than randomness. However, existing models are largely parametric and assume uncertain normal residuals, which often fail in practical applications involving nonlinear and non-normal dynamics. To address these limitations, we propose a nonlinear nonparametric uncertain autoregressive (NNUAR) model based on multidimensional Legendre polynomial approximation. This approach leverages tensor-product Legendre polynomials to nonparametrically capture nonlinear relationships, with parameters estimated via least squares. A two-stage framework is developed to address residual autocorrelation and departures from uncertain normality, incorporating an uncertain hypothesis test and cross-validation for optimal lag selection. Numerical experiments on two years of weekly closing prices of Ping An Bank show that the NNUAR model effectively captures complex nonlinear dependencies and significantly reduces residual correlation.