A Computational Multiresolution Nonlinear Autoregressive Framework Based on Wavelet Decomposition and Support Vector Regression

Abstract

This study introduces a computational multiresolution nonlinear autoregressive framework based on wavelet decomposition and support vector regression (SVR) for time series exhibiting heterogeneous temporal dynamics. Conventional nonlinear autoregressive models typically rely on single-scale lagged observations, which may be insufficient when the underlying process contains long-run movements, medium-term cycles, and short-term fluctuations simultaneously. To address this limitation, the proposed framework embeds discrete wavelet-based multiresolution representations of lagged observations directly into the autoregressive structure. The nonlinear relationship is estimated using ε-insensitive SVR with a Gaussian kernel, providing a flexible nonlinear learning mechanism. Model performance is assessed through an extensive Monte Carlo simulation design under several controlled data-generating environments, including multiscale dynamics, localized shocks, volatility clustering, and heavy-tailed disturbances. A rolling one-step-ahead forecasting scheme is employed for out-of-sample comparison with a conventional single-scale SVR benchmark. The simulation results indicate that incorporating multiresolution information improves forecasting accuracy across replications under the examined simulation settings. An empirical application to monthly copper price returns further illustrates the practical relevance of the proposed framework. Overall, the findings demonstrate the value of multiresolution representations in nonlinear autoregressive modeling of complex time series.