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.

翻译：本文针对BEKK-ARCH类高维波动率模型，提出了一种稳健且计算高效的估计框架。该方法通过数据截断确保对厚尾分布的稳健性，并利用正则化最小二乘法实现高维环境下的高效优化，这是通过利用BEKK-ARCH模型的等价VAR表示实现的。本文在厚尾机制下为所得估计量建立了非渐近误差界，并推导了极小极大最优收敛速率。此外，分别引入了稳健BIC准则和岭型估计量用于选择模型阶数和BEKK分量数量，并在厚尾设定下证明了其选择一致性。模拟研究验证了所提方法的有限样本性能，两个实证应用展示了其实际效用。结果表明，新框架在计算速度与预测精度方面均优于现有方法。