Xu Mengyu, Chen Xiaohui, Wu Wei Biao
Department of Statistics and Data Science, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA.
Department of Statistics, University of Illinois at Urbana-Champaign, S. Wright Street, Champaign, IL 61820, USA.
Entropy (Basel). 2019 Dec 31;22(1):55. doi: 10.3390/e22010055.
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained L 1 -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&P 500 index between 2003 and 2008.
本文关注高维非平稳时间序列的时变网络估计。考虑了两种动态行为：结构突变（即突变点）和平滑变化。为了同时处理这两种时变特征，提出了一种两步法：首先基于比较样本协方差矩阵上局部平均值的差异来识别多个突变点位置，然后基于核化时变约束(L_1)最小化逆矩阵估计（CLIME）估计器在每个片段上恢复图支撑。在温和的矩和相依条件下，我们推导了估计突变点和精度矩阵的收敛速度。特别地，我们表明在一定的高维缩放极限下，这种两步法在估计突变点和分段光滑精度矩阵函数方面是一致的。该方法应用于分析2003年至2008年标准普尔500指数的网络结构。
