高维向量自回归模型的速率最优鲁棒估计

Di Wang, R. Tsay
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引用次数: 11

摘要

在当前数据丰富的环境下,高维时间序列数据出现在许多科学领域。这类数据的分析给数据分析人员带来了新的挑战,不仅因为序列之间存在复杂的动态依赖关系,而且还存在异常观测值,如缺失值、污染观测值和重尾分布。对于高维向量自回归(VAR)模型,我们引入了一个统一的估计程序,该程序对模型错配、重尾噪声污染和条件异方差具有鲁棒性。该方法具有统计最优性和计算效率,可以处理稀疏、降秩、带状和网络结构VAR模型等高维模型。通过适当的正则化和数据截断,在有界$(2+2\epsilon)$ -th矩条件下,估计收敛速度在极小极大意义上几乎是最优的。当$\epsilon\geq1$时,收敛速度与亚高斯假设下的收敛速度相匹配。对于一些$\epsilon\in(0,1)$也建立了所提出的估计量的一致性,其中最小最大最优收敛率与$\epsilon$相关。通过仿真和美国宏观经济实例验证了所提估计方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rate-optimal robust estimation of high-dimensional vector autoregressive models
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is robust to model misspecification, heavy-tailed noise contamination, and conditional heteroscedasticity. The proposed methodology enjoys both statistical optimality and computational efficiency, and can handle many popular high-dimensional models, such as sparse, reduced-rank, banded, and network-structured VAR models. With proper regularization and data truncation, the estimation convergence rates are shown to be almost optimal in the minimax sense under a bounded $(2+2\epsilon)$-th moment condition. When $\epsilon\geq1$, the rates of convergence match those obtained under the sub-Gaussian assumption. Consistency of the proposed estimators is also established for some $\epsilon\in(0,1)$, with minimax optimal convergence rates associated with $\epsilon$. The efficacy of the proposed estimation methods is demonstrated by simulation and a U.S. macroeconomic example.
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