摘要:

Abstract.This paper provides a Bayesian approach to statistical inference in the threshold autoregressive model for time series. The exact posterior distribution of the delay and threshold parameters is derived, as is the multi‐step‐ahead predictive density. The proposed methods are applied to the Wolfe's sunspot and Canadian lynx data s

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00156.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.We consider the asymptotic distribution of the normalized periodogram ordinatesI(ωj)/f(ωj)(j= 1,2,…) of a general long‐memory time series. Here,I(ω;) is the periodogram based on a sample sizen,f(ω) is the spectral density and ωj= 2πj/n.We assume thatn→∝ withjheld fixed, and so our focus is on low frequencies; these are the most important frequencies for the periodogram‐based estimation of the memory parameterd.Contrary to popular belief, the normalized periodogram ordinates obtained from a Gaussian process are asymptotically neither independent identically distributed nor exponentially distributed. In fact, limn E{I(ωj)/f(ωj)}depends on bothjanddand is typically greater than unity, implying a positive asymptotic relative bias inI(ωj)as an estimator off(ωj).Tapering is found to reduce this bias dramatically, except at frequency ω1. The asymptotic distribution ofI(ωj)/f(ωj)for a Gaussian process is, in general, that of an unequally weighted linear combination of two independent X21random variables. The asymptotic mean of the log normalized periodogram depends onjanddand is not in general equal to the negative of Euler's constant, as is commonly assumed. Consequently, the regression estimator ofdproposed by Geweke and Porter‐Hudak will be asymptotically biased if the number of frequencies used in the regres

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00157.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.In this paper we consider bootstrap‐based predictive inference for autoregressive processes of orderp.We consider both unconditional inference and inference conditional on the lastpobserved values. We make two contributions. Our first contribution is to point out the best way to apply the bootstrap to unconditional predictive inference when the process is Gaussian. Now, it may be argued that predictive inference for autoregressive processes of orderpshould be carried out conditional on the lastpobserved values. When the process is Gaussian, a bootstrap predictive inference conditional on the lastpobserved values is conveniently computed by ‘running’ the same autoregressive process backwards in time. This procedure is inappropriate for non‐Gaussian autoregressive processes. Our second (and more important) contribution is to present a method (which is not computationally burdensome) for the computation of a bootstrap predictive inference for a non‐Gaussian autoregressive process of orderpconditional on the lastpobserv

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00158.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.We discuss the problem of estimating the transfer function and an autoregressive model for measurement noise in a linear system. A parameterization that is often more parsimonious than the usual ARX model is used. Particular emphasis is given to the selection of model orders when it is not assumed that the true system is finitely parameterized. Consistency of the transfer function and noise spectrum estimates is established using a new uniform convergence law for an appropriate class of martingale transforms.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00159.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.For stationary second‐order autoregressive normal processes, the conjecture of uniqueness of the solution of the exact likelihood equations is examined. A sufficient condition for uniqueness is given; this condition is satisfied with very high probability if the number of observations is not extremely small. Moreover, it is shown that not more than two maxima may exist. Examples of data which actually produce a likelihood function with two local maxima are give

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00160.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.We look at the implications of modeling observations from a fractionally differenced noise process using an approximating AR (p) model. The approximation is used because of computational difficulties in the estimation of the differencing parameter of the fractional noise model. Because the fractional noise process is long‐range dependent, we assess the applicability of the approximating autoregressive (AR) model based on its long‐range forecasting accuracy compared with that of the fractional noise model. We derive the asymptotick‐step‐ahead prediction error for a fractional noise process modeled as an AR(p) process and compare it with thek‐step‐ahead prediction error obtained when the model for the observed series is correctly specified as a fractional noise process and the fractional differencing parameterdis either known or estimated. We also assess the validity of the asymptotic results for a finite sample size via simulation. We see that AR models can be useful for long‐range forecasting of long‐memory data, provided that consideration is given to the forecast horizon when choosing an appr

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00161.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.Maximum likelihood estimation of sampled continuous‐time stochastic processes is considered. The likelihood is directly maximized with respect to the original structural parameters using a scoring algorithm with exact analytical derivatives. Furthermore, the case of unobserved states and errors of measurement is treated via EM and quasi‐Newton algorithms. The proposed methods are illustrated with simulation studies and analysis of sunspot activ

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00162.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

Abstract.The average Fisher information about the parameter of a finite‐order ARMA process is non‐singular if and only if the parameter is identifia

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00163.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00164.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1993.tb00165.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY