Integrated Heteroskedastic Nonlinear Vector Autoregression

Abstract

Reservoir computing (RC) provides a lightweight framework for nonlinear time-series forecasting, with Nonlinear Vector Autoregression (NVAR) offering a deterministic alternative through polynomial transformations of time-delay embeddings. However, its least squares-based ridge readout may be sensitive to heteroskedastic and stochastic disturbances common in financial and economic series.This paper introduces Integrated Heteroskedastic Nonlinear Vector Autoregression (IHNVAR), a variance-aware extension of NVAR that incorporates estimated conditional residual variances into an iteratively reweighted multi-output readout. The weighting framework is variance-model agnostic. For this study, GARCH(1, 1) estimates from step-ahead residuals are used. A one-shot weighted variant, NVAR-WLS, isolates the contribution of weighting from iteration.IHNVAR is evaluated under univariate endogenous direct multi-horizon forecasting across financial, macroeconomic, volatility, and electricity-price series against NVAR, NVAR-WLS, naive, autoregressive, and LSTM benchmarks. Results show that variance-aware estimation is most effective when recoverable nonlinear structure coexists with predictable heteroskedastic noise and the applied weighting mechanism aligns with the forecast-error structure. Polynomial expansion may instead introduce noise-sensitive interactions when stochastic innovations dominate, while weighting may be ineffective or detrimental under irregular, horizon-misaligned, or informative variance. Most gains arise from the initial reweighting step, with iteration providing secondary, dataset-dependent improvements.Overall, IHNVAR is positioned as a conditional robustness extension of NVAR whose effectiveness depends on nonlinear signal strength, stochastic noise, predictable variance, and forecast-horizon alignment.