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自回归模型的递归估计AI 解读

SUMMARY This paper is concerned with the recursive estimation of autoregressive models, in particular the realtime determination of the order of such a specification. A model selection criterion based on the minimum description length principle due to Rissanen is discussed and strong consistency in the stationary situation is shown. Alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the…

未来与过去之间的单位典型相关AI 解读

Stationary vector ARMA processes $x(t), t = 0, \pm 1, \pm 2, \cdots$, of $n$ components are considered that are of full rank, and the situation where there are linear functions of the future $x(t), t > 0$, and the past $x(t), t \leq 0$ (more properly the present and the past) that have unit correlation. It is shown that the number of linearly independent such pairs (i.e., the number of unit canonical correlations between future and past) is the number of zeros of the…

ARMA 参数估计的回归方法AI 解读

Regression procedures for parameter estimation in autoregression moving average (ARMA) models are discussed, mainly for providing initial estimates for iterative maximization of a Gaussian likelihood. An iterative procedure of Spliid (1983) is compared to a procedure of Hannan and Rissanen (1982), and a global convergence result is established for an iterative modification of Spliid's procedure. Spliid's iteration does not always converge; when it does, it has the same…

ARMA 估计的回归程序AI 解读

Regression procedures for parameter estimation in autoregression moving average (ARMA) models are discussed, mainly for providing initial estimates for iterative maximization of a Gaussian likelihood. An iterative procedure of Spliid (1983) is compared to a procedure of Hannan and Rissanen (1982), and a global convergence result is established for an iterative modification of Spliid's procedure. Spliid's iteration does not always converge; when it does, it has the same…

线性系统的递归估计AI 解读

The estimation of parameters for a scalar linear system with rational transfer function is considered, the estimates being updated each time a new data point comes to hand. Two well-known algorithms are compared by simulation with a method related to the three-stage algorithm of Hannan & Rissanen (1982); a computation scheme using Givens transformations is proposed which makes the three-stage recursive algorithm economical. A central limit theorem is proved for the…

线性系统的递归估计AI 解读

The estimation of parameters for a scalar linear system with rational transfer function is considered, the estimates being updated each time a new data point comes to hand. Two well-known algorithms are compared by simulation with a method related to the three-stage algorithm of Hannan & Rissanen (1982); a computation scheme using Givens transformations is proposed which makes the three-stage recursive algorithm economical. A central limit theorem is proved for the…

自回归移动平均模型的一种估计方法AI 解读

The problem considered is that of estimating an autoregressive-moving average system, including estimating the degrees of the autoregressive and moving average lag operators. The basic method is that introduced by Hannan & Rissanen (1982). However, that method may sometimes overestimate the degrees and modifications are here introduced to correct this. The problem is itself due to the use of a long autoregression, of order clogT when T is large, in the first stage of the…

一种自回归移动平均模型估计方法AI 解读

The problem considered is that of estimating an autoregressive-moving average system, including estimating the degrees of the autoregressive and moving average lag operators. The basic method is that introduced by Hannan & Rissanen (1982). However, that method may sometimes overestimate the degrees and modifications are here introduced to correct this. The problem is itself due to the use of a long autoregression, of order clogT when T is large, in the first stage of the…

自相关、自回归与自回归逼近AI 解读

Theorems are proved relating to the rate of almost sure convergence of autocovariances, and hence autocorrelations, to their true values. These rates are uniform in the lag up to some order $P(T)$, increasing with $T$. The key assumption is that the process is stationary and the best linear predictor is the best predictor. In particular for an ARMA process and $P(T) = O\{(\ln T)^a\}, a < \infty$, the rate is $O\{(\ln \ln T/T)^{1/2}\}$. These results are used to discuss…

ARMA 过程阶数的估计AI 解读

Under general conditions strong consistency of certain estimates of the maximum lags of an autoregressive moving average process is established. A theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of over-estimation of a maximum lag is evaluated.

基于 ARMA 模型的递归估计AI 解读

A recursive estimate of the stochastic structure of a stationary time series is constructed based on the assumption that the true structure is ARMA, i.e., has a rational spectrum. The estimate is recursive in the sense that each successive estimate is obtained from the previous one by a relatively simple adjustment, that could be effected in a "real time" situation. The procedure is basically that of updating a regression when all variates involved are constructed from…

关于自回归移动平均模型识别的一则札记AI 解读

A discussion is given of the identification and parameterization of autoregressive-moving average systems in relation to the use of certain canonical forms.

自回归模型阶数的确定AI 解读

Summary It is shown that a strongly consistent estimation procedure for the order of an autoregression can be based on the law of the iterated logarithm for the partial autocorrelations. As compared to other strongly consistent procedures this procedure will underestimate the order to a lesser degree.

自回归移动平均系统识别的一则札记AI 解读

A discussion is given of the identification and parameterization of autoregressive-moving average systems in relation to the use of certain canonical forms.

预测误差方差的估计AI 解读

Spectral methods are used to construct an estimate of the variance of the prediction error for a normal, stationary process. The estimate obtained is shown to be strongly consistent and asymptotically normally distributed. Some aspects of the computations with respect to the fast Fourier transform are considered. The latter half of the article consists of a number of simulations, based on both generated and real data, which illustrate the results obtained. The relation…

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…

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.

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.

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.