论文标题
小波协方差的渐近正态性和多元小波值估计器的渐变性
Asymptotic normality of wavelet covariances and of multivariate wavelet Whittle estimators
论文作者
论文摘要
具有远距离依赖性属性的多元过程可以在许多应用程序领域遇到。此类框架中的两个基本特征是远程依赖参数和组件时间序列之间的相关性。我们考虑多元远程依赖性线性过程，不一定是高斯。我们表明，在这种情况下，小波系数之间的协方差是渐近的高斯。我们还研究了长距离依赖参数的估计值的渐近分布以及基于小波的晶体过程的长期协方差。我们证明了估计量的渐近正态性，并为渐近协方差提供了明确的表达。在大鼠大脑连接性的真实数据集上提出了对此结果的经验例证。
Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time series. We consider multivariate long-range dependent linear processes, not necessarily Gaussian. We show that the covariances between the wavelet coefficients in this setting are asymptotically Gaussian. We also study the asymptotic distributions of the estimators of the long-range dependence parameter and the long-run covariance by a wavelet-based Whittle procedure. We prove the asymptotic normality of the estimators, and we provide an explicit expression for the asymptotic covariances. An empirical illustration of this result is proposed on a real dataset of rat brain connectivity.
