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序列协方差的渐近分布AI 解读

A central limit theorem is proved for the sample serial covariances of an ergodic, stationary, purely nondeterministic process whose linear innovations have their first four moments as for a sequence of independent random variables. The necessary and sufficient condition for the theorem is then that the spectra be square integrable.

ARMA 模型的估计AI 解读

In estimating a vector model, $\Sigma B(j)x(n-j)=\Sigma A(j)\epsilon(n-j), A(0)=I_r, E(\epsilon(m)\epsilon(n)')=\delta_{mn}K$ it is suggested that attention be confined to cases where $g(z) =\Sigma A(j)z^j, h(z)=\Sigma B(j)z^j$ have determinants with no zeroes inside the unit circle and have $I_r$ as greatest common left divisor and where $\1brack A(p)\vdots B(q) \rbrack$ is of rank r, where p, q are the degrees of g, h, respectively. It is shown that these conditions ensure…

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群时延的估计AI 解读

It is suggested that in estimating spectra and cross spectra for a pair of stationary series the estimation of the phase may be replaced by an estimate of the group delay, which is the derivative of phase with respect to frequency. An estimate is proposed and its asymptotic properties are investigated. The results are illustrated by simulation and by application to real data. The estimation of a group delay that is constant over a nondegenerate band is also discussed.

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未知滞后长度的滞后回归AI 解读

Summary The problem considered is that of determining the parameters in a lagged regression of one stationary time series on another when the lag is unknown and is not an integral multiple of the time interval between observations. The residual in the regression is also taken to be a stationary time series. The method of estimation is based on the maximization with respect to the lag of a form of autocorrelation between the two series. However, the autocorrelation is defined…

群时延估计AI 解读

It is suggested that in estimating spectra and cross spectra for a pair of stationary series the estimation of the phase may be replaced by an estimate of the group delay, which is the derivative of phase with respect to frequency. An estimate is proposed and its asymptotic properties are investigated. The results are illustrated by simulation and by application to real data. The estimation of a group delay that is constant over a nondegenerate band is also discussed.

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相干性与群时延的估计AI 解读

The usual estimation of coherence is known to be badly biased towards zero if over the band of frequencies used for its estimation the phase is changing rapidly, as in the case of large group delay. The usual asymptotic distribution theory for spectral estimates is of no value in this circumstance, since it does not involve the group delay. A new theory is used to obtain estimates of coherence and group delay, which is itself of considerable physical interest, and the…

含移动平均误差的多方程系统的识别问题AI 解读

where y(t) and x(t) are vectors of G components, z(t) has K components, B is a G x G matrix, and F is a G x K matrix.' The components of z(t) are predetermined at time t and the vector x(t) is not serially correlated, so that (among other requirements) we have

相干性与群延迟的估计AI 解读

The usual estimation of coherence is known to be badly biased towards zero if over the band of frequencies used for its estimation the phase is changing rapidly, as in the case of large group delay. The usual asymptotic distribution theory for spectral estimates is of no value in this circumstance, since it does not involve the group delay. A new theory is used to obtain estimates of coherence and group delay, which is itself of considerable physical interest, and the…

混合移动平均与自回归系统的估计AI 解读

Estimates are constructed of the parameters in mixed moving average autoregressive models based upon Fourier transformation of the data. These are shown to be asymptotically normal with the same distribution as the maximum likelihood estimators for the Gaussian case. The method extends to the vector case but the procedure is discussed in detail only for vector moving averages.

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混合移动平均自回归系统的估计AI 解读

Estimates are constructed of the parameters in mixed moving average autoregressive models based upon Fourier transformation of the data. These are shown to be asymptotically normal with the same distribution as the maximum likelihood estimators for the Gaussian case. The method extends to the vector case but the procedure is discussed in detail only for vector moving averages.

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向量时间序列中最小二乘估计的效率AI 解读

Summary A theorem due to Rosenblatt (1959) concerning the circumstances under which least squares is asymptotically efficient for the estimation of the matrix of regression parameters in a system of regressions is re-formulated in a simpler form and is extended. A theorem is proved relating to the efficiency of least squares under linear constraints which is not specifically of a time series nature.

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滞后回归关系的估计AI 解读

The paper discusses a technique for estimating the matrices of coefficients, B(j), in a regression relation relating a vector time series, z(n), to lagged values, y(n—j), —p ≤ j ≤ q, of a second vector time series. The technique depends upon calculation of spectra and cross-spectra. Once these are computed the estimates B(j) are obtained successively without recalculation when an additional lag is introduced. When the residuals from the regression are generated by a linear…