线性平稳序列的自相关分析

本文的目的在于,对于线性平稳时间序列的样本、自协方差、自相关和偏相关函数的渐近性质,给出一个比较系统的描述.以下内容将是被论及到的,上述样本函数的矩的性质,渐近正态分布,强相容性和几乎处处收敛的速度等.我们将给出在上述诸方面的某些重要的新的成果,这些结果都是在时间序列分析的文献中被建立起来的,与此同时,我们还对其中比较深的结果给出详细的数学推导.文中的绝大部分内容,都曾做为硕士研究生的时间序列课程的一部分被使用过.

Autocorrelation analysis of linear stationary time series

The aim of this paper is to give a systematic account of asymptotic properties of the sample autocovariance, autocorrelation and partial autocorrelation functions of linear stationary time series. The subjects of property of moments,asymptotic normal distribution, strong consistence and almost sure convergent rate for these sample functions, will be concered.We shall provide some important and new results on these subjects, which are by now well-established in the time series literature, and at the same time we shall provide the detailed mathematical derivation of the deeper results.Most of the material in this paper has been used as a part of the course of time series analysis for M.S.students.