摘要
Many authers have studied the asymptotic behavior of the integral periodogram of a Gaussian stationary series. In this paper, the invariance principle for the integral periodogram of a multiple time series is investigated. We have obtained the following theorem:Let X, be a real M -dimensional stationary time series with spectral density matrix f(λ) which satis-fies the conditions:M,and X, can be represented in theform: Xn =whereξ, is the M-dimensional fourth order moment existedstationary martingale series, thenweakly converges to a Gauss process η(λ) withEη(λ) = 0,where V and Q are the second and fourth moment of the martingale seriesξ , respectively.From this theorem, two corollaries have been given, which cover some results of [2][5][6].
Many authers have studied the asymptotic behavior of the integral periodogram of a Gaussian stationary series. In this paper, the invariance principle for the integral periodogram of a multiple time series is investigated. We have obtained the following theorem:Let X, be a real M -dimensional stationary time series with spectral density matrix f(λ) which satis-fies the conditions:M,and X, can be represented in theform: Xn =whereξ, is the M-dimensional fourth order moment existedstationary martingale series, thenweakly converges to a Gauss process η(λ) withEη(λ) = 0,where V and Q are the second and fourth moment of the martingale seriesξ , respectively.From this theorem, two corollaries have been given, which cover some results of [2][5][6].
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1992年第1期 102-113,共12页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
