ASYMPTOTIC THEORY FOR SPECTRAL DENSITY ESTIMATES OF GENERAL MULTIVARIATE TIME SERIES
ASYMPTOTIC THEORY FOR SPECTRAL DENSITY ESTIMATES OF GENERAL MULTIVARIATE TIME SERIES
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DOI：
10.1017/s0266466617000068
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发表时间：
2018-02
影响因子：
0.8
通讯作者：
W. Wu;P. Zaffaroni
中科院分区：
文献类型：
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作者：
W. Wu;P. Zaffaroni
对于由任意可测的iid新息函数表示的一般多元平稳过程，我们得到了滞后窗谱密度估计的一致收敛结果。最佳的收敛速度，持有的时间序列和横截面尺寸发散，得到温和的和容易验证的条件下。我们的理论补充了早期的结果，其中大部分是单变量的，主要关注的概率，弱收敛或分布收敛，但在一组更强的正则性条件下，如线性iid创新。基于互谱密度函数，我们提出了一个新的测试之间的独立性平稳时间序列。我们还解释了在何种程度上我们的结果提供了基础，以获得双渐近结果估计的广义动态因子模型。
We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability, weak or distributional convergence, yet under a much stronger set of regularity conditions, such as linearity in iid innovations. Based on cross spectral density functions, we then propose a new test for independence between two stationary time series. We also explain the extent to which our results provide the foundation to derive the double asymptotic results for estimation of generalized dynamic factor models.