Covariance matrix estimation and linear process bootstrap for multivariate time series of possibly increasing dimension
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维度可能增长的多元时间序列协方差估计与线性过程自助法
- 研究问题
- 多元时间序列的维度随样本量增长时，如何一致估计自协方差结构，并构造适用于样本均值推断的自助法？
- 方法与思路
- 作者将自协方差矩阵序列堆叠，以平顶渐缩权重估计大矩阵，再据此将单变量线性过程自助法扩展到多变量。
- 材料陈述的贡献
- 摘要称，协方差估计在维度增长时仍一致，自助法对固定或增长维度的样本均值渐近有效；固定维度下还适用于谱密度估计。
- 阅读关注点
- 应核对依赖条件、维度增长速度、矩阵估计与重采样步骤，并区分样本均值和谱密度结果的适用范围。
- 阅读边界
- 仅据版本未注明的索引摘要，维度增长上限和一般假设未说明；模拟中的较好表现仅限部分情形，不能认定普遍优越。
原文摘要
Multivariate time series present many challenges, especially when they are high dimensional. The paper’s focus is twofold. First, we address the subject of consistently estimating the autocovariance sequence; this is a sequence of matrices that we conveniently stack into one huge matrix. We are then able to show consistency of an estimator based on the so-called flat-top tapers; most importantly, the consistency holds true even when the time series dimension is allowed to increase with the sample size. Second, we revisit the linear process bootstrap (LPB) procedure proposed by McMurry and Politis [ J. Time Series Anal. 31 (2010) 471–482] for univariate time series. Based on the aforementioned stacked autocovariance matrix estimator, we are able to define a version of the LPB that is valid for multivariate time series. Under rather general assumptions, we show that our multivariate linear process bootstrap (MLPB) has asymptotic validity for the sample mean in two important cases: (a) when the time series dimension is fixed and (b) when it is allowed to increase with sample size. As an aside, in case (a) we show that the MLPB works also for spectral density estimators which is a novel result even in the univariate case. We conclude with a simulation study that demonstrates the superiority of the MLPB in some important cases.