A robust and scalable framework for high-dimensional volatility estimation

TL;DR

This paper presents a new robust, scalable framework for high-dimensional volatility estimation in BEKK-ARCH models, combining data truncation, regularization, and model selection techniques.

Contribution

It introduces a novel estimation approach with non-asymptotic error bounds, minimax optimal rates, and consistent model selection under heavy-tailed distributions.

Findings

Outperforms existing methods in speed and accuracy

Provides finite-sample error bounds and convergence rates

Demonstrates effectiveness through simulations and empirical applications

Abstract

This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed distributions and utilizes a regularized least squares method for efficient optimization in high-dimensional settings. This is achieved by leveraging an equivalent VAR representation of the BEKK-ARCH model. Non-asymptotic error bounds are established for the resulting estimators under heavy-tailed regime, and the minimax optimal convergence rate is derived. Moreover, a robust BIC and a Ridge-type estimator are introduced for selecting the model order and the number of BEKK components, respectively, with their selection consistency established under heavy-tailed settings. Simulation studies demonstrate the finite-sample performance of the proposed method, and two empirical applications illustrate its practical utility. The results show that the new framework outperforms existing alternatives in both computational speed and forecasting accuracy.