摘要:

Abstract.In this paper we study the estimation of the spectral density functions of a continuous‐time parameter almost periodically correlated process from one discrete random‐time sampling. Under mixing hypotheses on the cumulant of the process, we establish the quadratic consistency of this estimator and the rate of converge

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00286.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.A time series model representing a decomposition into permanent plus transient components contains a deterministic component when the signal‐to‐noise ratio is equal to zero; otherwise, the permanent component is said to be stochastic. This distinction has important consequences in the analysis of economic phenomena. On the other hand, the absence of a stochastic permanent component in residuals from a time series regression may indicate cointegration. This paper considers the frequency domain estimation of the signal‐to‐noise ratio in a representative of the unobserved components model class. The sampling properties of the estimator from the resulting approximate spectral likelihood differ from those observed in the time domain and they vary substantially depending on whether the overall slope must be estimated or not. Further, it is shown that spectral estimates areT‐consistent—instead ofT2‐consistent in the time domain. These results may explain some of the differences in estimators from frequency domain approximations to the likelihood and exact maximum likelihood estimators, and may be of use when testing for determi

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00287.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.A functional limit theorem with a particular function class and topology is derived for non‐ergodic type time series. This limit theorem allows us to study the asymptotic law of the associated likelihood ratio test (LRT) statistic for testing the presence of a change in the covariance parameter in the explosive Gaussian autoregressive model. We show that the level of the LRT cannot be approximated without introducing appropriate normalization. The limit law of a particular weighted likelihood ratio test is examined through a simulation study and is compared with the well‐known Kolmogorov distribution obtained in the stationary case; we conclude that for practical applications when the root is really close to unity one can use the same thresholds as in the stationary case. This procedure is applied to the study of three real time series known to be non‐stati

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00288.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.In this paper we develop a test procedure for detecting overdifferencing or a moving‐average unit root in time series regression models with Gaussian autoregressive moving‐average errors. In addition to an intercept term the regressors consist of stable or asymptotically stationary variables and non‐stationary trending variables generated by an integrated process of order 1. The test of the paper is based on the theory of locally best invariant unbiased tests. Its limiting distribution is derived under the null hypothesis and found to be non‐standard but free of unknown nuisance parameters. Asymptotic critical values, which depend on the number of integrated regressors, are obtained by simulation. A limited simulation study is carried out to illustrate the finite sample properties of t

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00289.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.In this paper an outlier test for contaminated autoregressive processes is introduced. The test is based on a comparison of each observation with a predictor using past and future values, a so‐called two‐sided predictor. It is required that an upper bound for the total number of outliers is known.The asymptotic distribution of the test statistic is calculated under the null hypothesis that no outlier is present. The behaviour of the test for finite sample size is investigated by a simulation study. Moreover, the test is compared with several other outlier te

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00290.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.This paper presents an optimal predictor of level crossings, catastrophes, for autoregressive moving‐average processes, and investigates the performance of the predictor. The optimal catastrophe predictor is the predictor that gives a minimal number of false alarms for a fixed detection probability. As a tool for evaluating, comparing and constructing the predictors a method using operating characteristics, i.e. the probability of correct alarm and the probability of detecting a catastrophe for the predictor, is used. An explicit condition for the optimal catastrophe predictor based on linear prediction of future process values is given and compared with a naive catastrophe predictor, which alarms when the predicted process values exceed a given level, and with some different approximations of the optimal predictor. Simulations of the different algorithms are presented, and the performance is shown to agree with the theoretical results. All results indicate that the optimal catastrophe predictor is far better than the naive predictor. They also show that it is possible to construct an approximate catastrophe predictor requiring fewer computations without losing too much of the optimal predictor performanc

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00291.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY