摘要:

Abstract.The expectation‐maximization algorithm is reviewed briefly. The algorithm is applied to time series situations where outliers may be present. An approximation of the algorithm is considered to reduce the computational complexity. Examples are given to illustrate the application of this algorith

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00140.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.An estimator of the difference parameter in a class of long‐memory time series models is examined. It is shown that, in particular circumstances, the estimator can be badly biased, and tests based on it consequently seriously misleading. The source of this bias is identified, and it is shown that its magnitude can readily be predicted through straightforward analytical argument

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00141.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.The limiting process of partial sums of residuals in stationary and invertible autoregressive moving‐average models is studied. It is shown that the partial sums converge to a standard Brownian motion under the assumptions that estimators of unknown parameters are root‐nconsistent and that innovations are independent and identically distributed random variables with zero mean and finite variance or, more generally, are martingale differences with moment restrictions specified in Theorem 1. Applications for goodness‐of‐fit and change‐point problems are considered. The use of residuals for constructing nonparametric density estimation is

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00142.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.Letxtbe a time series generated by an autoregressive integrated moving‐average process ARIMA(p, d, q). The non‐overlapping aggregate series also follows an ARIMA process. Thus, the prediction of the aggregated observations could be done by either the disaggregate model or the aggregate model. We derive the efficiency of the predictors for two important disaggregate models, ARIMA(0, 1, 1) and ARIMA(0, 2, 2), when the models are assumed known. When the models are not known we estimate the efficiency through simulation with the models being selected using Akaike's information criter

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00143.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.We develop a small‐sample criterion (AICC) for the selection of the order of vector autoregressive models. AICCis an approximately unbiased estimator of the expected Kullback‐Leibler information. Furthermore, AICCprovides better model order choices than the Akaike information criterion in small samp

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00144.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.I consider continuous‐time autoregressive processes of orderpand develop estimators of the model parameters based on Yule‐Walker type equations. For continuously recorded data, it is shown that these estimators are least squares estimators and have the same asymptotic distribution as maximum likelihood estimators.In practice, though, data can only be observed discretely. For discrete data, I consider approximations to the continuous‐time estimators. It is shown that some of these discrete‐time estimators are asymptotically biased. Alternative estimators based on the autocovariance function are suggested. These are asymptotically unbiased and are a fast alternative to the maximum likelihood estimators described by Jones. They may also be used as starting values for maximum likelihood est

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00145.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.In this paper we discuss some properties of non‐stationary autoregressive moving‐average processes with Λ‐stationary (0<Λ<2) stable innovations. Linear forecasts and the dispersion of theh‐steps‐ahead forecast error are obtained and some examples are given. The problem of parameter estimation i

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00146.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.It is shown that a multivariate linear stationary process whose coefficients are absolutely summable is invertible if and only if its spectral density is regular everywhere. This general characterization of invertibility is applied later to the case of a linear process having an autoregressive moving‐average (ARMA) representation. Under the usual assumptions, it is deduced that a processYdescribed by an ARMA(φ, TH) model is invertible if and only if the polynomial detTH(z) has no roots on the unit circle. Given an invertible processYwhich has an ARMA representation, it is finally shown that the processYT, whereYT, =εi=0lSiYt‐i, is invertible if and only if the matrixS(z) =εi=0lSiziis of full rank for allzof modulus 1. It follows, in particular, that any subprocess of an invertible ARMA process is also inve

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00147.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.In this paper we consider the long‐run distribution of a multivariate autoregressive process of the formxn=An‐1xn‐1+ noise, where the noise has an unknown (possibly nonstationary and nonindependent) distribution andAnis a (generally) time‐varying transition matrix. It can easily be shown that the processxnneed not have a known long‐run distribution (in particular, central limit theorem effects do not generally hold). However, if the distribution of the noise approaches a known distribution asngets large, we show that the distribution ofxnmay also approach a known distribution for largen.Such a setting might occur, for example, when transient effects associated with the early stages of a system's operation die out. We first present a general result that applies for arbitrary noise distributions and generalAn. Several special cases are then presented that apply for noise distributions in the infinitely divisible class and/or for asymptotically constant coefficientAn. We illustrate the results on a problem in characterizing the asymptotic distribution of the estimation error in a Kalm

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00148.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY