多维平稳时间序列积分谱图的不变原理

用积分周期图估计平稳时间序列的谱函数，不论是高斯序列还是非高斯序列，其误差过程的不变原理都已被证明，许重光采用自迥归谱估计的积分估计谱函数也证明了误差过程的不变原理成立。本文讨论多维平稳时间序列，引进积分谱图来估计谱函数，证明了误差过程的不变原理在较弱的条件下成立。积分周期图是积分谱图的特例，因而［１］［３］［６］的一些结果是本文有关定理的特例。

INVARIANCE PRINCIPLE FOR THE INTEGRAL SPECTROGRAPH OF A MULTIPLE STATIONARY TIME SERIES

By using integral periodogram to estimate the spectral functions of a stationary time series, the invariance principle for the error process has been demonstrated either for Gaussian or non-Gaussian series.[1],[2],[5]This paper is devoted to investigating the multiple time series,introduce the integral spectrograph to estimate the spectral functions. The invariance principle for the error process is also valid for either Gaussian or non-Gaussian series.The integral periodogram is a special case of the integral spectrograph, some main results of [1],[2] [5] are the special case of this paper.