摘要:

Abstract.LetXt=c0Yt+c1Yt‐1+… be a linear process with known coefficientsck, whereYtis a strict white noise. Letm1, …,m2rbe given numbers. A method is presented to determine whether there exists a distribution ofYtsuch thatEXkt=mkfork= 1, …, 2r. In the positive case, such a distribution ofYtis described. Some explicit formulas for AR(1) and AR(2) models are derived. The results can be used for simulating a process with given moments of its stationary distribution. The procedure also enables proof that some stationary distributions cannot belong to the given linear

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00001.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.An estimator of the spectral density of a stationary process is obtained by approximating it with a step function. The positions of the level changes are determined using partitioning algorithms. The algorithms are stopped by using criteria such as AIC. In examples, the resulting estimates are shown to be good representations of the true spectra in most circumstances, even when the series are fairly short. In particular the estimates highlight spikes in the spectral density that are caused by periodicities.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00002.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.In this paper, we investigate different representations of bilinear models introduced by Granger and Andersen (1978). We consider first the decomposition of these models on the chaos of Wiener, then we give for the subdiagonal models al‐Markovian representation, generalizing a result obtained by Pham Dinh (1985) in the case of the superdiagonal models. Thus we consider the polynomial state affine representation. For these representations, we are interested in the existence and the uniqueness of the decomposition and the expression of the different moments of the model

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00003.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.The problem of testing randomness against specified and unspecified contiguous ARMA alternatives is considered. In the case of specified alternative, the linear serial rank tests proposed by the authors (Hallin, Ingenbleek and Puri 1985) are shown to be asymptotically most powerful within the class of all possible tests (at the required level). In the case of unspecified alternative, however, any of the above optimal tests is unfortunately completely insensitive against a whole subclass of the alternative.Quadratic serial rank statistics, providing tests of the χ2‐type are therefore introduced. Their asymptotic distributions are derived, under the null hypothesis as well as under contiguous ARMA alternatives. The asymptotically maximin most powerful quadratic serial rank tests (for a given density) are then obtained. Because of their close similarity with the Box‐Pierce parametric test, we call themrank portmanteau tests. The asymptotic relative efficiencies (AREs) of the rank portmanteau tests with respect to one another and their AREs with respect to the corresponding Box‐Pierce and quadratic Spearman tests are d

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00004.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.It is shown that oscillatory sequences and slowly changing processes are strongly harmonizable. Their theoretical harmonizable spectra are also derived.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00005.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.Shannon interpolation is used to assign values from a readily simulated discrete time process to the times of a point process, simulated by Ogata's thinning technique. The result is a set of unequally spaced samples from a hypothetical continuous time process with spectrum equal to that of the discrete time process for frequencies |ω| ≤π/Δ and identically equal to zero for |ω|>π/Δ, where Δ is the discrete time step. The spectra are theoretically known both for the sampled process and for the sampling point process. We calculate Brillinger spectral estimates for examples of a process with autoregressive spectrum, sampled at the times of a Hawkes Self Exciting Point Process. The success of the Brillinger estimator is demonstrated but it is shown to have an inherently high variance. An approximate confidence interval is d

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00006.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.We obtain an integral equation recurrence relation for the optimal least squares predictor of a nonlinear autoregressive time series model. Numerical solutions are given for a first order threshold model up to three steps ahead.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00007.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.An approach to the analyses of discrete‐valued time series is discussed. The analyses are accomplished in the spectral domain using the Walsh‐Fourier transform which is based on Walsh functions. This approach will enable an investigator of discrete systems to analyse the data in terms of square waveforms and sequency rather than sine waves and frequency.We develop a general signal‐plus‐noise type model for discrete‐valued time series in which Walsh‐Fourier spectral analysis is of interest. We consider the problems of detecting whether a common signal exists in repeated measures on discrete‐valued time series and in discrete‐valued processes collected in an experimental design. We show that these models may depend on unknown regression parameters and we develop consistent estimates of these parameters based on the finite Walsh‐Fourier transform. Applications to certain Markov models are given; however, the methods presented also apply to

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00008.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.On the basis of the asymptotic behaviour of autoregressive parameter estimates, the properties of autoregressive spectral density estimates are deduced. The simultaneous confidence bands for the spectra are derived using Šidák's inequality. Simulation experiments are used to illustrate the quality of the derived confidence band

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00009.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY

摘要:

Abstract.Box and Tiao (1977) established the correspondence between non‐stationary roots and canonical correlations of an AR(1) process. In this paper, we give an alternative, more direct, proof of the correspondence and extend a special case of that result to AR(p) processes. The usefulness of these results for multiple time series modelling is also briefly discusse

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1987.tb00010.x

出版商:Blackwell Publishing Ltd    

年代:1987

数据来源: WILEY