摘要:

Abstract.Performance of the state dependent model developed by Priestley is evaluated relative to that of bilinear and standard linear models using two well‐known time series. The results indicate the use of broader classes of time series models beyond the conventional ARMA class is likely to lead to significant reductions in forecasting error. However, there are difficult problems relating to the identification of the order of the model, estimation of the parameters, and determination of the correct nonlinear mode

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1985.tb00410.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

Abstract.In this paper the asymptotic behaviour of Bartlett'sUp‐statistic for a goodness‐of‐fit test for stationary processes, is considered. The asymptotic distribution of the test process is given under the assumption that a central limit theorem for the empirical spectral distribution function holds. It is shown that theUp‐statistic tends to the supremum of a tied down Brownian motion. By a counterexample we refute the conjecture that this distribution is in general of the Kolmogorov‐Smirnov type. The validity of the central limit theorem for the spectral distribution function is then discussed. Finally a goodness‐of‐fit test for ARMA‐processes based on the estimated innovation sequence is given, and it is shown that this test statistic is asymptotically Kolmogorov‐Sm

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1985.tb00411.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

Abstract.A rigorous analysis is given of the asymptotic bias of the log maximum likelihood as an estimate of the expected log likelihood of the maximum likelihood model, when a linear model, such as an invertible, gaussian ARMA (p, q) model, with or without parameter constraints, is fit to stationary, possibly non‐gaussian observations. It is assumed that these data arise from a model whose spectral density function either (i) coincides with that of a member of the class of models being fit, or, that failing, (ii) can be well‐approximated by invertible ARMA (p, q) model spectral density functions in the class, whose ARMA coefficients are parameterized separately from the innovations variance. Our analysis shows that, for the purpose of comparing maximum likelihood models from different model classes, Akaike's AIC is asymptotically unbiased, in case (i), under gaussian or separate parametrization assumptions, but is not necessarily unbiased otherwise. In case (ii), its asymptotic bias is shown to be of the order of a number less than unity raised to the power max {p, q} and so is negligible if max {p, q} is not too small. These results extend and complete the somewhat heuristic analysis given by Ogata (1980) for exact or approximating autoregressive mod

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1985.tb00412.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

Abstract.Whittle has obtained an optimality property of a method of estimation of the parameter of the spectrum. In this paper we present a proof in the vector parameter case. Gaussian estimation is a natural method to consider, based on finite Fourier transforms and periodograms.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1985.tb00413.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

Abstract.In this paper we utilize martingale theorems to obtain central limit theorems for the finite Walsh‐Fourier transforms of various second‐order stationary proces

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1985.tb00414.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY

摘要:

Abstract.State estimation and prediction problems are considered for a stochastic process represented by a state space form which involves unknown parameters. We first study the stability of the Kalman filter corresponding to the state space form without assuming the stationarity of the process. Second, we consider the state estimation and prediction when the process is stationary, and show some asymptotic properties of the state estimates and predicted values obtained by the Kalman filter with estimated parameters which converge to the true parameters or to the equivalent classes of the true parameters with probability one.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1985.tb00415.x

出版商:Blackwell Publishing Ltd    

年代:1985

数据来源: WILEY