摘要:

Abstract.Given length‐nsampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, inn, that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross‐moments of the non‐centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovari

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00280.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.An algorithm for recursive computation of the parameters of periodic autoregressive moving‐average (ARMA) processes is given. It also provides recursions for stationary multivariate ARMA processes. A procedure for simultaneous estimation of the order and the parameters of a periodic ARMA process is outline

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00281.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.Estimating low or high frequencies is usually more difficult than estimating ordinary frequencies. In this paper, we show that the estimation accuracy depends on the combination of frequency, phase and sample size. For the best case, the mean square error can be smaller than the standard asymptotic Cramèr–Rao bound for an unbiased estimator in the Gaussian white noise case. Asymptotic theory for two limit procedures—the frequency changes as sample size increases or the frequency is fixed while the signal to noise ratio (SNR) increases—is established. Simulation shows that this theory is relevant for a wide range of situations which vary from small sample size (10) and high SNR (≥ 4) to large sample size (1000) and low SNR

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00282.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.This paper deals with the third‐order asymptotic theory for Gaussian autoregressive moving‐average (ARMA) processes with unknown meanμ.We are interested in the estimation ofρ= (α1…, αp, β1…, βq), whereα1…,αρandβ1…,βqare the coefficients of the autoregressive part and the moving‐average part, respectively. First, we investigate the third‐order asymptotic optimality of the bias adjusted maximum likelihood estimator (MLE) ofρin the presence of the nuisance parameters μ and s̀2(innovation variance). Next, for a Gaussian AR(1μμ, s̀2), we propose a mean corrected estimator αc1c2of the autoregressive coefficient. We make a comparison between the bias adjusted estimator αc1c2* and the bias adjusted MLE, in terms of their probabilities of concentration around the true value, or equivalently, in terms of their mean squared errors. Finally some numerical studies are provided in order to verify

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00283.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.This paper derives expressions for the exact bias and variance of a general class of spectral density estimators at the zero frequency, building on the work of Neave (The exact error in spectrum estimates.Ann. Math. Statist.42 (1971), 961–75) who studied the case where the mean of the series is assumed known. These expressions are evaluated for 15 different windows and for a wide variety of stationary time series. The exact error of the estimators is found to depend on whether the sample mean has to be estimated, and some windows are noticeably inferior at certain values of the bandwidth. A response surface analysis reveals that the finite sample relationships between the bandwidth and the exact error are quite different from the ones suggested by asymptotic theor

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00284.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.The problem of computing estimates of the state vector when the Kalman filter is seeded with an arbitrarily large variance is considered. To date the response in the literature has been the development of a number of relatively complex hybrid filters, usually involving additional quantities and equations over and above the conventional filter. We show, however, that a certain square root covariance filter is capable of handling the complete range of variances (zero, positive and infinite) without modification to the filtering equations themselves and without additional computation loads. Instead of the more conventional Cholesky factorization, our filter employs an alternative matrix factorization procedure based on a unit lower triangular matrix and a diagonal matrix. This permits the use of a modified form of fast Givens transformations, central to the development of an efficient algorithm.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00285.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY