摘要:

Abstract.Asymptotic distributions of the autoregressive parameters in the AR(2) model are derived, when the characteristic polynomial has a pair of complex roots on the unit circle. Percentage points are tabulated based on simulations from the asymptotic formulae. The usefulness of the asymptotic results in finite sample situations is investigated by a Monte Carlo study, and an illustrative example is given.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00416.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.An estimation and inference procedure is proposed for parameters of thepth order autoregressive model with roots both on the unit circle and outside the unit circle. The procedure is motivated by the fact that the parameter estimates of the nonstationary part of the model have higher order consistency properties than the parameter estimates of the stationary part. The procedure allows the use of the known asymptotic distributional results of purely nonstationary models and purely stationary models. Only ordinary least squares routines are needed.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00417.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.A cross‐validated form of Whittle's frequency domain approximation to the likelihood function of a stationary Gaussian process is described, and proposed as a criterion for choosing the bandwidth in a kernel spectrum estimate. The criterion is shown to be equivalent, in large samples, to the mean integrated squared error. The statistical properties of the spectrum estimate whose bandwidth maximizes the criterion have been explored in a limited simulatio

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00418.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.The axis‐crossing counts in a time series and in its successive differences are called higher‐order crossings (HOC). Under the Gaussian assumption the sequence of expected HOC is monotone increasing and admits a spectral representation which establishes a clear connection between HOC and the spectrum. In particular the normalized number of axis‐crossings (first HOC) tends to admit values at or near a dominant frequency, while the sequence of normalized HOC converges to the highest frequency in the spectrum. When the series is first lowpass filtered, the resulting normalized HOC tend to ‘visit’ true discrete frequencies on their way to the highest frequency. If the successive differences are replaced by successive summation, the resulting modified normalized HOC converge monotonically to the lowest frequency in the

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00419.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.LetYn=μ+Σβj(Yn–j–μ) +ɛnbe apth order autoregressive process with innovations {ɛn} in the domain of attraction of a stable law with index αmax(1, α). In addition, some statements are made regarding estimators of α which will give the full (Hannan and Kanter) rate of conv

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00420.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.The paper provides a method for the computation of the derivatives of the exact log likelihood function of a Gaussian time series. Based on this result and using Fisher's scoring technique, an efficient method for computing the maximum likelihood estimates for an autoregressive moving average model has been obtained. Simulations suggest that the new procedure is as fast as the Box and Jenkins conditional least squares method. In a similar way, a procedure is derived to compute the Lagrange multiplier test statistics for testing the goodness of fit of the model.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00421.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.In this paper the large sample behaviour of the sample autocorrelation matrixRn(h), (hbeing the lag,nthe sample size), of a multivariate autoregressive time series with one of its characteristic roots equal to unity and the rest of the roots lying inside the unit circle is studied. It is shown thatRn(h) converges almost surely to a constant matrix. Further, the asymptotic distribution ofRn(h) is characterized as that of a random matrix which is a function of jointly normal random variables.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00422.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.The algorithm proposed here is a multivariate generalization of a procedure discussed by Pearlman (1980) for calculating the exact likelihood of a univariate ARMA model. Ansley and Kohn (1983) have shown how the Kalman filter can be used to calculate the exact likelihood function when not all the observations are known. In Shea (1983) it is shown that this algorithm is much quicker than that of Ansley and Kohn (1983) for all ARMA models except an ARMA (2, 1) and a couple of low‐order AR processes and therefore when we have no missing observations this algorithm should be used instead. The Fortran subroutine G13DCF in the NAG (1987) Library fits a vector ARMA model using an adaptation of this algorithm. Experience in the use of this routine suggests that having reasonably good initial estimates of the ARMA parameter matrices, and in particular the residual error covariance matrix, can not only substantially reduce the computing time but more important improve the convergence properties of the minimization procedure. We therefore propose a method of calculating initial estimates of the ARMA parameters which involves using a generalization of the concept of inverse cross covariances from the univariate to the multivariate case. Finally theory is put into practice with the fitting of a bivariate model to a couple of real‐life time ser

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00423.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.In this note, we shall investigate third‐order asymptotic properties of BLUE and LSE for a regression model with ARMA residual. In the first place we shall evaluate the asymptotic mean square errors of BLUE and LSE up to third order. For appropriate regression variables (constant or harmonic functions), the asymptotic mean square error of LSE coincides with that of BLUE up to second order. Then we shall evaluate the difference of the asymptotic mean square errors of LSE and BLUE at third order. Secondly we shall show that BLUE is third‐order asymptotically efficient in the sense of the highest probability concentration around the true value in the third‐order Edgeworth expa

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00424.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.We propose the logistic transformation as an appropriate instantaneous transformation for time series variables known to be bounded, such as those measured as proportions, and present an application to two unemployment rate series. Since such series are often analysed in logarithmic form, the two transformations are compared, and a likelihood ratio selection criterion is developed, which marginally favours the logistic transformation. We consider the question of transformation bias and its removal. The logistic transformation of bounded variables ensures consistency with the limiting behaviour and is symmetric, thus on transforming and modelling the unemployment rate or its complement, the employment rate, equivalent results are obtained.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00425.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY