Nonparametric GARCH: An Iterated Neural Estimator
Abstract
We study nonparametric estimation and forecasting for GARCH-type processes and propose an iterated neural estimator that alternates between estimating the recursion map and updating the unobserved conditional variances. Under mild conditions, we establish finite-sample bounds for the time-averaged in-sample variance-path error and show that the estimator is minimax rate-optimal up to logarithmic factors. Under stationarity and mixing conditions, we establish the same rate for recursion-map estimation and derive finite-sample bounds for out-of-sample variance forecasts and expected excess Gaussian quasi-likelihood (QLIKE) loss. The convergence rates depend on the true lag orders and remain unchanged when the fitted orders are overspecified. Simulation studies illustrate the effectiveness of our estimators under nonlinear and time-varying volatility dynamics. Real-data applications suggest that our neural methods perform competitively and can incorporate option-price and high-frequency information.
Related
- Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis
- Optimal Neural Estimation for High-Dimensional Nonparametric Regression under Multisource Covariate Shift
- Sharp Generalization for Nonparametric Regression in Interpolation Space by Shallow Over-Parameterized Neural Networks with Channel Attention
- Structured SDEs for Realized GARCH: Continuous-Time Volatility Modelling and Component-Level Analysis
- Forecasting Non-Fungible Token (NFT) Market Volatility Through Hybrid GARCH–LSTM Models
BibTeX
@misc{deng2026nonparametric,
title = {{Nonparametric GARCH: An Iterated Neural Estimator}},
author = {Ruizhi Deng and Guohao Shen and Ngai Hang Chan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04157},
eprint = {2611.04157},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04157},
}
RIS
TY - UNPB
TI - Nonparametric GARCH: An Iterated Neural Estimator
AU - Ruizhi Deng
AU - Guohao Shen
AU - Ngai Hang Chan
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04157
UR - https://arxiv.org/abs/2611.04157
AB - We study nonparametric estimation and forecasting for GARCH-type processes and propose an iterated neural estimator that alternates between estimating the recursion map and updating the unobserved conditional variances. Under mild conditions, we establish finite-sample bounds for the time-averaged in-sample variance-path error and show that the estimator is minimax rate-optimal up to logarithmic factors. Under stationarity and mixing conditions, we establish the same rate for recursion-map estimation and derive finite-sample bounds for out-of-sample variance forecasts and expected excess Gaussian quasi-likelihood (QLIKE) loss. The convergence rates depend on the true lag orders and remain unchanged when the fitted orders are overspecified. Simulation studies illustrate the effectiveness of our estimators under nonlinear and time-varying volatility dynamics. Real-data applications suggest that our neural methods perform competitively and can incorporate option-price and high-frequency information.
ER -