摘要:

Abstract.Weiss (J. Appl. Prob.12 (1975) 831–36) has shown that for causal autoregressive moving‐average (ARMA) models with independent and identically distributed (i.i.d.) noise, time‐reversibility is essentially unique to Gaussian processes. This result extends to quite general linear processes and the extension can be used to deduce that a non‐Gaussian fractionally integrated ARMA process has at most one representation as a moving average of i.i.d. random variables with finite variance. In the proof of this uniqueness result, we use a time‐reversibility argument to show that the innovations sequence (one‐step prediction residuals) of an ARMA process driven by i.i.d. non‐Gaussian noise is typically not independent, a result of interest in deconvolution problems. Further, we consider the case of an ARMA process to which independent noise is added. Using a time‐reversibility argument we show that the innovations of the ARMA process with added independent noise are independent if and only if both the driving noise of the process and the added noi

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00114.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.Spectral analysis is a well‐established procedure for detecting harmonic signals in a noisy environment. Much research has been done on methods that use second‐order statistics (i.e. the autocovariance function and power spectrum) such as Whittle's test, Bartlett's test, Hannan's test and the PriestleyP(Λ) test. When the noise is non‐Gaussian, statistics of order greater than two can provide more information to detect the periodicities in noisy data. We direct our main attention to the third (fourth) order cumulant and bispectral (trispectral) methods. New test statistics are derived and are shown to be more powerful than other methods based on second‐order statistics under a mixed spectrum condition. The asymptotic power functions of the new test statistics and other tests are studied. Some Monte Carlo simulations are used to evaluate the performance of the new methods with moderate samp

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00115.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.A state space model with diffuse initial conditions is considered. A simple and direct proof of the algorithm for computing the likelihood function and minimum mean square estimators of the state is given

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00116.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.In this paper we consider the vector autocorrelation approach for identifying ARMA (p, q) models and use a bootstrap procedure in order to evaluate the distribution of the corresponding sample statistics by means of a resampling scheme for the residuals whenpandqare unknown. The asymptotic validity of the bootstrap procedure applied to the vector autocorrelation estimates is established. Some simulations and examples demonstrating the appropriateness of the proposed bootstrap procedure in comparison with large‐sample Gaussian approximations are include

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00117.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.The test for white noise proposed by Reschenhofer (Biometrika76 (1989) 629–32) is adaptive in that the form of its test statistic depends on the data. It proceeds (i) by using the real part of the finite Fourier transform of the data for the selection of the form of the test statistic and (ii) by applying the selected test statistic to the imaginary part.In this paper it is shown that independently of using information contained in the real part to construct a test statistic for the imaginary part, information contained in the imaginary part can be used to construct a test statistic for the real part. Because of the independence of these tests, they can easily be combined.Then a further test is proposed which again is adaptive but where both the real and imaginary parts contribute simultaneously to a single test statisti

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00118.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.In this paper we consider techniques of spectral analysis for stationary point processes in order to study the behaviour of a complex physiological system. The estimates of the power spectrum are obtained by smoothing the periodogram which is computed very rapidly with the help of the fast Fourier transform algorithm. In the computation of the estimates we can use either the whole record of the data or a number of disjoint records.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00119.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.The asymptotic bias to terms of orderT‐1, whereTis the observed series length, is studied for estimators of the coefficients and disturbance variance in an AR(p) model. Reduction of the asymptotic bias by tapering is established and, if the tapering function is defined appropriately to depend onT, not only is the asymptotic bias reduced, but the asymptotic distribution of the estimators is not altered. In addition, the asymptotic biases of other time series parameter estimators constructed from the sample covariance function, such as several types of spectral estimators, can also be reduced by taperin

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00120.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY