FACTOR MODELING FOR HIGH-DIMENSIONAL TIME SERIES: INFERENCE FOR THE NUMBER OF FACTORS
FACTOR MODELING FOR HIGH-DIMENSIONAL TIME SERIES: INFERENCE FOR THE NUMBER OF FACTORS
复制标题
DOI：
10.1214/12-aos970
复制
发表时间：
2012-04-01
影响因子：
4.5
通讯作者：
Yao, Qiwei
中科院分区：
文献类型：
--
作者：
Lam, Clifford;Yao, Qiwei
本文从降维的角度研究了高维时间序列的因子建模问题。在固定的设置下，推断是简单的，在这个意义上，无论是因素的数量和因素负载的估计在一个非负定矩阵的特征分析，因此适用于当时间序列的维度是在几千的顺序。在两种情况下，研究了该方法的渐近性质：（i）当时间序列维数固定时，样本量趋于无穷大;（ii）样本量和时间序列维数同时趋于无穷大.特别是，我们的估计为零特征值享受更快的收敛（或更慢的发散）率，从而使估计的因素的数量更容易。特别地，当样本容量和时间序列的维数一起趋于无穷大时，特征值的估计不再是相容的。然而，我们的估计因子的数量，这是基于估计的特征值的比率，仍然工作得很好。此外，这种估计显示了所谓的“祝福的维度”属性的意义上，估计的性能可能会提高时，时间序列的维数增加。一个两步的程序进行了研究时，因素是不同程度的强度。数值模拟和真实的数据说明也报告。
This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are estimated in terms of an eigenanalysis for a nonnegative definite matrix, and is therefore applicable when the dimension of time series is on the order of a few thousands. Asymptotic properties of the proposed method are investigated under two settings: (i) the sample size goes to infinity while the dimension of time series is fixed; and (ii) both the sample size and the dimension of time series go to infinity together. In particular, our estimators for zero-eigenvalues enjoy faster convergence (or slower divergence) rates, hence making the estimation for the number of factors easier. In particular, when the sample size and the dimension of time series go to infinity together, the estimators for the eigenvalues are no longer consistent. However, our estimator for the number of the factors, which is based on the ratios of the estimated eigenvalues, still works fine. Furthermore, this estimation shows the so-called "blessing of dimensionality" property in the sense that the performance of the estimation may improve when the dimension of time series increases. A two-step procedure is investigated when the factors are of different degrees of strength. Numerical illustration with both simulated and real data is also reported.