摘要:

Abstract.This paper is concerned with statistical inference of nonstationary and non‐invertible autoregressive moving‐average (ARMA) processes. It makes use of the fact that a derived process of an ARMA(p, q) model follows an AR(q) model with an autoregressive (AR) operator equivalent to the moving‐average (MA) part of the original ARMA model. Asymptotic distributions of least squares estimates of MA parameters based on a constructed derived process are obtained as corresponding analogs of a nonstationary AR process. Extensions to the nearly non‐invertible models are considered and the limiting distributions are obtained as functionals of stochastic integrals of Brownian motions and Ornstein‐Uhlenbeck processes. For application, a two‐stage procedure is proposed for testing unit roots in the MA polynomial. Examples are given to illustrate the

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00261.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.Some general properties of long memory continuous time processes are recalled or proved. Methods of simulation are studied. A comparison with the usual discrete time autoregressive fractionally integrated moving‐average filter is made and illustrations are provided. Then, two methods of estimation of the parameters of such a model from a discrete sample are studied, both theoretically and empirically, with Monte Carlo experiment

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00262.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.This paper shows numerically that the lack of power and size distortions of the Dickey‐Fuller type tests for unit roots (very well documented in the unit root literature) are similar to and in many situations even smaller than the lack of power and size distortions of the standard Studentttests for stationary roots of an autoregressive mode

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00263.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.The kernel smoothing method has been considered as a useful tool for identification and prediction in time series models. In practice this method is to be tuned by a smoothing parameter. For selection of the smoothing parameter, Härdle and Vieu (Kernel regression smoothing of time series.J. Time Ser. Anal.13(1992), 209–32) considered a cross‐validation rule and proved its asymptotic optimality. In this paper we strengthen their result for a wider use of the kernel smoothing of time se

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00264.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.In this paper, the information between the past and the future of a Gaussian stationary sequence is calculated either by its spectral density or by its autocovariances, and is related to the problem of model fitting. It is demonstrated that the criterion of minimum mutual information is the generalization of that of maximum entropy. By employing the above information quantity, we propose a procedure, which is called LIC for simplicity, to obtain consistent estimate of the order of the Bloomfield model or the autoregressive model. In Monte Carlo studies, we illustrate the LIC procedure by several examples, and also estimate the spectral density of time series by the Bloomfield model and LIC method.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00265.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.One of the key features of wavelet analysis is its potential use for effecting time‐frequency decompositions of non‐stationary signals. The relationship between wavelet analysis and time‐dependent spectral analysis has so far rested mainly on heuristic reasoning:in this paper we examine the relationship in a more precise mathematical form. A crucial feature of this analysis is the need to define carefully the notion of “frequency” when applied to non‐station

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00266.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.The residual autocorrelations in nonstationary autoregressive processes with autoregressive characteristic roots on the unit circle are considered. Limiting distributions of the residual autocovariances and the residual autocorrelations are shown to be the same as the limiting distributions when parameters are estimated with all roots on the unit circle known. The portmanteau statistic is shown to have a x2limiting distribution. The Canadian lynx data set is analysed to illustrate our theory. The portmanteau test seems also useful when the characteristic roots are close to the unit circle.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00267.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY