摘要:

Abstract.A simplified version of the square root Kalman filter is obtained for a vector autoregressive moving‐average (VARMA) model. The algorithm is computationally more efficient that the standard square root algorithm and its output can be used to compute the likelihood of a VARMA model accuratel

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00050.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.General linear processes do not usually satisfy strong mixing conditions. Therefore, we investigate the empirical process based on samples from such a general linear process by using a truncation argument and derive a local fluctuation inequality. It is well known that such a fluctuation inequality is of basic importance in the study of the empirical process. Here it is applied to obtain a rate of almost sure (a.s.) convergence for certain density estimators in the supremum norm. This extends a local result obtained by Chanda. As a direct corollary a rate of a.s. convergence for a mode estimator is obtained.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00051.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.The asymptotic zero‐crossing rate (ZCR) of the general second‐order autoregressive process is investigated. When the associated characteristic polynomial has a unit rooteiθ(0 ≤θ≤π), the ZCR converges in mean square to θ/π and the rate of convergence is very fast regardless of the

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00052.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.The problem of estimation of the parameterbin the simple diagonal bilinear model {Xt},Xt=et+bet‐1Xt‐1, is considered, where {et} is Gaussian white noise with zero mean and possibly unknown variance s̀2. The asymptotic normality of the moment estimator ofbis established for the two cases when s̀2is known and s̀2is unknown. It is noted that the limit distribution of the least‐squares cannot easily be derived analytically. A bootstrap comparison of the sampling distributions of the least‐squares and moment estimates shows that both are asymptotically normal with the least‐squares estimate being the mo

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00053.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.Two procedures are described for obtaining Fisher's information matrix of a multiplicative seasonal autoregressive‐moving average process. They can be useful in determining the asymptotic covariance matrix of Gaussian maximum likelihood estimators of the parameters. Components of the information matrix are expressed in the first procedure as integrals of rational functions. The second procedure makes use of the autocorrelation function of several autoregressive processe

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00054.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.We discuss the parameter identification of multivariate AR (1) models and of univariate ARMA (2,1) and AR (2) models if the variables in the model are observed everymth period wheremis some integer greater than unity. The results indicate that the models will often not be globally identified even if they are locally identified and that the likelihood function can have a large number of local maxima.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00055.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.Expressions for the bias of the least‐squares and modified Yule‐Walker estimators in a correctly specified multivariate autoregression of arbitrary order are obtained without assuming that the innovations are Gaussian. Instead, the innovations are assumed to form a martingale difference sequence which is stationary up to sixth order and which has finite sixth moments. The errors in the expressions are shown to be O(n‐3/2), as the sample sizenunder some moment conditions. The expressions obtained are the same in the Gaussian and non‐Gaussia

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00056.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY

摘要:

Abstract.A general approach for the development of a statistical inference on autoregressive moving‐average (ARMA) models is presented based on geometric arguments. ARMA models are characterized as members of the curved exponential family. Geometric properties of ARMA models are computed and used to suggest parameter transformations that satisfy predetermined properties. In particular, the effect on the asymptotic bias of the maximum likelihood estimator of model parameters is illustrated. Hypothesis testing of parameters is discussed through the application of a modified form of the likelihood ratio test statisti

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1990.tb00057.x

出版商:Blackwell Publishing Ltd    

年代:1990

数据来源: WILEY