Qiu Huitong, Xu Sheng, Han Fang, Liu Han, Caffo Brian
Johns Hopkins University, 615 N. Wolfe St., Baltimore, MD 21210 USA.
Princeton University, 98 Charlton Street, Princeton, NJ 08544 USA.
JMLR Workshop Conf Proc. 2015 Jul;37:1843-1851.
Gaussian vector autoregressive (VAR) processes have been extensively studied in the literature. However, Gaussian assumptions are stringent for heavy-tailed time series that frequently arises in finance and economics. In this paper, we develop a unified framework for modeling and estimating heavy-tailed VAR processes. In particular, we generalize the Gaussian VAR model by an elliptical VAR model that naturally accommodates heavy-tailed time series. Under this model, we develop a quantile-based robust estimator for the transition matrix of the VAR process. We show that the proposed estimator achieves parametric rates of convergence in high dimensions. This is the first work in analyzing heavy-tailed high dimensional VAR processes. As an application of the proposed framework, we investigate Granger causality in the elliptical VAR process, and show that the robust transition matrix estimator induces sign-consistent estimators of Granger causality. The empirical performance of the proposed methodology is demonstrated by both synthetic and real data. We show that the proposed estimator is robust to heavy tails, and exhibit superior performance in stock price prediction.
高斯向量自回归（VAR）过程在文献中已得到广泛研究。然而，高斯假设对于金融和经济中频繁出现的重尾时间序列来说过于严格。在本文中，我们开发了一个用于建模和估计重尾VAR过程的统一框架。具体而言，我们通过椭圆VAR模型对高斯VAR模型进行了推广，该模型自然地适用于重尾时间序列。在这个模型下，我们为VAR过程的转移矩阵开发了一种基于分位数的稳健估计器。我们表明，所提出的估计器在高维情况下实现了参数收敛速率。这是分析重尾高维VAR过程的第一项工作。作为所提出框架的一个应用，我们研究了椭圆VAR过程中的格兰杰因果关系，并表明稳健转移矩阵估计器会产生格兰杰因果关系的符号一致估计器。所提出方法的实证性能通过合成数据和真实数据得到了证明。我们表明，所提出的估计器对重尾具有稳健性，并且在股票价格预测中表现出卓越的性能。
