摘要:

Abstract.Consider a stationary non‐negative autoregressive (AR) model givenxt=b1xt‐1, +…+bpxt‐p+et, where theetare independent identically distributed non‐negative variables andb1, …,bpare non‐negative parameters, and all the roots of the equation 1 –b1u–…–bpup= 0 are outside the unit circle. The stationary solution of the above AR model is called a stationary non‐negative AR process. Letx1,x2, …xnbe an example of a stationary non‐negative AR process. Under very general conditions strongly consistent estimators of the AR parametersb1,b2, …,bphave been studied. In this paper a new procedure is proposed to estimate not onlyb1,b2, …,bpbut alsobowhich is the essential lower bound of the variableet. We shall show that the new estimators obtained using the new procedure are consistent estimators ofbo,b1, …,bpunder the weakest condition which guarantees that the stationary non‐negative AR model has a s

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00108.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.In this paper we develop an asymptotic theory for application of the bootstrap to stationary stochastic processes of autoregressive moving‐average (ARMA) type, with known order (p, q). We give a proof of the asymptotic validity of the bootstrap proposal applied to M estimators for the unknown parameter vector of the process. For this purpose we derive an asymptotic expansion for M estimators in ARMA models and construct an estimate for the unknown distribution function of the residuals which in principle are not observable. A small simulation study is also include

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00109.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.We provide a stochastic proof of the inequality ρ(A⊗A+B⊗B) ≥ρ(A⊗A), where ρ(M) denotes the spectral radius of any square matrixM, i.e. max{|eigenvalues| ofM}, andM⊗Ndenotes the Kronecker product of any two matricesMandN.The inequality is then used to show that stationarity of the bilinear modelwill imply stationarity of the linear part, i.e. the linear ARMA modelforr= 1 andq= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model withbij=0 fori

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00110.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.Within the context of likelihood and Bayes approaches to inference in autoregressive moving‐average (ARMA) time series models, previous ideas on parameter transformation and numerical integration for implementing Bayesian procedures are reviewed. Some novel transformation ideas are introduced and their role in an efficient numerical integration approach is examined. Some comparisons of the effectivesness of different numerical integration strategies are mad

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00111.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.The canonical correlation between the past and future of a stationary time series is shown to be the limit of the canonical correlation between the infinite past and finite future, and computation of the latter is reduced to an eigenvalue problem invovling finite matrices. This provides a convenient finite‐dimensional algorithm for computing canonical correlations and components of a time series. An upper bound is conjectured for the largest canonical correlatio

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00112.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Abstract.The nonstationary multivariate autoregressive (AR) model Φ (L)Yt=εtis considered for anm‐dimensional process {Yt}, where it is assumed that det {Φ(L)}= 0 hasd

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1992.tb00113.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY