Convergence of covariance and spectral density estimates for high-dimensional locally stationary processes
本文为高维局部平稳过程的时间变化二阶统计量估计建立了系统的渐近理论，推导了依赖于样本量、维数、矩条件和过程依赖性的收敛速度，对计量经济学和统计学研究者有参考价值。
Covariances and spectral density functions play a fundamental role in the theory of time series. There is a well-developed asymptotic theory for their estimates for low-dimensional stationary processes. For high-dimensional nonstationary processes, however, many important problems on their asymptotic behaviors are still unanswered. This paper presents a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of high-dimensional locally stationary processes. Using the framework of functional dependence measure, we derive convergence rates of the estimates which depend on the sample size $T$, the dimension $p$, the moment condition and the dependence of the underlying processes.