摘要:

Abstract.In time series analysis of data sequences, the estimation of the parameters of an identified autoregressive moving‐average (ARMA) model is a well‐known and straightforward exercise. However, if the parameters of the model are periodic (i.e. a periodic ARMA (PARMA) model) then the estimation process becomes more difficult. This paper describes an on‐line parameter estimation technique, based on methods from automatic control, which is demonstrated to provide consistent estimates of PARMA model param

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00226.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.Testing the null hypothesis that a process is difference stationary has received considerable attention in the past decade. Recently, there has been some interest in testing the null hypothesis that a process is a sum of a linear trend and a stationary invertible noise sequence. In this paper we present procedures for testing the null hypothesis that a process is trend stationary against the alternative that the process is difference stationary. A Monte Carlo study is presented to study the behavior of the proposed test criteria. Average global temperature data are used to illustrate the test criteria.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00227.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.We develop a simple test for testing equality of variances for paired stationary Gaussian time series. The test statistic is a modifiedzstatistic. It is based on the periodograms of the two series and consistent estimation of the difference between the two spectral densities. Simulations illustrate the validity of the asymptotic results for finite samples. An application to EEG data is discussed.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00228.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.We consider bootstrap construction and calibration of prediction intervals for nonGaussian autoregressions. In particular, we address the question of prediction conditioned on the lastpobservations of the process, for which we offer an exact simulation technique and an approximate bootstrap approach. In simulations for a variety of first‐order autoregressions, we compare various nonparametric prediction intervals and find that calibration gives reasonably narrow prediction intervals with the lowest coverage probability mean squared error among the methods use

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00229.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.Stochastic modeling on the basis of established deterministic formulations is stressed and some examples from seismology are presented. Using well‐known deterministic models for a source time function, a single parameter stochastic difference equation (autoregressive model) is derived for seismic records of P‐waves from nuclear explosions and natural earthquakes. A model‐evaluation technique other than statistical goodness‐of‐fit is considered, and its application is illustrated using available data. The interdependency between the characteristic polynomial of the difference equation, its complementary solution (signal), its particular integral (noise) and some physical variables are explained. Variables included in the discussion are duration, intensity and the so‐called corner frequency. Utilizing these dependencies, the signal‐generated character of noise is also illustrated.To fit the model an estimation procedure is described, and its statistical properties are derived. It is shown that the proposed model fits the records of P‐waves from underground nuclear explosions and natural earthquakes as well as the records of Rayleigh waves from atmospheric explosions. Applications of the model to depth‐ and reflection‐parameter estimation and to event discrimination are discussed, and some representative numerical exa

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00230.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.Researchers are sometimes faced with a set of observations that constitute a sparse coverage of a time series, suspected to be periodic. The period is unknown, but one can identify in the observed data a few points that are presumed to occur at the same phase, in different cycles of the unknown periodicity. We propose an algorithm that finds all periods which are compatible with such observed data, and suggest how to assess their statistical significance. The algorithm also provides stringent limits on the epochs of the fixed phase. We give three examples, from the field of astronomy, for application of our new algorithm. In the first one the algorithm reveals, on the basis of very few photometric observations, a highly significant period in the light curve of the recent classical Nova Herculis 1991. In the second example, in the series of arrival times of neutrinos from the supernova SN1987A, our algorithm yields a definite negative result. It proves that no significant exact periodicity is present in the data. In the third application, the algorithm provides new constraints on the epoch of one of the minima in the light curve of the stellar binary system 44i Bootis. We compare the method with other period search techniques, pointing out a few of its advantages, as well as some of its weaknesses.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00231.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.An alternative derivation is given of results first obtained by Porat (1987) concerning the asymptotic efficiencies of sample autocovariances of a stationary Gaussian ARMA process. This is based on an approximation to the likelihood of these autocovariances.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00232.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY