Joint convergence of sample autocovariance matrices when $p/n\to 0$ with application

Consider a high-dimensional linear time series model where the dimension $p$ and the sample size $n$ grow in such a way that $p/n\to 0$ . Let $\hat{\Gamma }_{u}$ be the $u$ th order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$ exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with some additional effort, implies the asymptotic normality of the trace of any polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$ . We also study similar results for several independent MA processes. We show applications of the above results to statistical inference problems such as in estimation of the unknown order of a high-dimensional MA process and in graphical and significance tests for hypotheses on coefficient matrices of one or several such independent processes.Consider a high-dimensional linear time series model where the dimension $p$ and the sample size $n$ grow in such a way that $p/n\to 0$. Let $\hat{\Gamma }_{u}$ be the $u$th order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$ exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with some additional effort, implies the asymptotic normality of the trace of any polynomial in $\{\hat{\Gamma }_{u},\hat{\Gamma }_{u}^{*},u\geq 0\}$. We also study similar results for several independent MA processes. We show applications of the above results to statistical inference problems such as in estimation of the unknown order of a high-dimensional MA process and in graphical and significance tests for hypotheses on coefficient matrices of one or several such independent processes.

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笔记与分组

分类依据与纠错

Joint convergence of sample autocovariance matrices when $p/n\to 0$ with applicationJoint convergence of sample autocovariance matrices when $p/n\to 0$ with application

代码、数据与补充材料

维度与样本量之比趋零时样本自协方差矩阵的联合收敛及应用

原文摘要

同方向的基础文献

同方向的基础文献

分类依据与纠错

Joint convergence of sample autocovariance matrices when p/n→0p/n\to 0p/n→0 with applicationJoint convergence of sample autocovariance matrices when $p/n\to 0$ with application

代码、数据与补充材料

维度与样本量之比趋零时样本自协方差矩阵的联合收敛及应用

原文摘要

同方向的基础文献

同方向的基础文献

Joint convergence of sample autocovariance matrices when $p/n\to 0$ with applicationJoint convergence of sample autocovariance matrices when $p/n\to 0$ with application