A1131
Title: Deep nonparametric estimation for volatility functions via iterative algorithms
Authors: Ruizhi Deng - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Guohao Shen - The Hong Kong Polytechnic University (Hong Kong)
Ngai Hang Chan - City University of Hong Kong (Hong Kong)
Abstract: A novel approach is introduced to estimating nonparametric GARCH models using deep neural networks. An efficient iterative algorithm is proposed for training these deep estimators, characterized by ease of implementation and adaptability to various model settings and loss functions. Learning guarantees for the proposed method are established, including non-asymptotic upper bounds on prediction error under mild assumptions. Notably, it is demonstrated that the deep neural network estimator can adapt to the true lag dimension of the volatility model even when the input dimension is overspecified. This crucial property ensures optimal performance even with suboptimal input choices. The effectiveness of the approach through extensive simulations is validated, showcasing its superiority over competing methods, particularly in high-dimensional, nonlinear, and complex volatility scenarios.
