摘要:

Abstract.This paper considers the long memory Gegenbauer autoregressive movingaverage (GARMA) process that generalizes the fractionally integrated ARMA (ARFIMA) process to allow for hyperbolic and sinusoidal decay in autocorrelations. We propose the conditional sum of squares method for estimation (which is asymptotically equivalent to the maximum likelihood estimation) and develop the asymptotic theory. Many results are in sharp contrast to those of the ARFIMA model. Simulations are conducted to assess the performance of the proposed estimators in small sample applications. Two applications to the sunspot data and the US inflation rates based on the wholesale price index are provided.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00268.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.In this paper we are concerned with the robustness of inferences, carried out on a stationary process contaminated by a small trend, to this departure from stationarity. It is shown that a smoothed periodogram approach to model fining and parameter estimation is highly robust to the presence of a small trend if the underlying stationary process is short‐range dependent. If the underlying process is long‐range dependent the robustness properties are still good but now depend on the Hurst index of the process and deteriorate with increasing Hurst in

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00269.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.Beveridge and Nelson (A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle.J. Monet. Econ.7 (1981), 151–74) introduced a decomposition into trend plus irregular components for time series generated by models that are integrated of order one. The components are functions of current and past, but not future, values of the series. Therefore, these components can be viewed as estimates available to an agent at the time. Moreover, the decomposition exists whenever the generating process is stationary after first differencing. In this paper we extend the decomposition to generating processes that are integrated of order two, and to the seasonal models of Box and Jenkins (Time Series Analysis, Forecasting and Control.San Francisco:Holden Day, 1970). The analysis leads to the estimation of stochastic growth rates, as well as component series. The methodology is applied to monthly UK industrial production dat

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00270.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.In this paper we discuss the spectral analysis of a stationary bivariate point process applied to the study of a complex physiological system. An estimate of the cross‐spectral density can be obtained by smoothing the modified cross‐periodogram statistic. The smoothed estimate is calculated by dividing the whole length of the data into a number of disjoint subrecords. Estimates of the coherence function and the cross‐intensity function follow directly from the estimate of the cross‐spectral density. It is shown that the asymptotic properties of the estimate of the cross‐intensity function can be improved by inserting a convergence factor in it. Examples of the estimates are illustrated by using two data sets from neurophysiological experiments and their importance is emphasized by examining the behaviour of the complex physiological system un

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00271.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.An approximating sequence of Markov processes with transitions at times 0, 1/n, 2/n,…, wherenis large, was used in Brockwell and Hyndman (On continuous time threshold autoregression.Int. J. Forecasting8 (1992), 157–73) and Brockwell (On continuous time threshold ARMA processes.J. Stat. Planning Inference39 (1994). 291–304) to fit continuous time threshold autoregressive moving‐average (CTARMA) models with boundary width 2δ>0 to both simulated and real data. In this paper we approximate CTARMA processes with δ= 0 by a new sequence of continuous processes and show that the distribution and conditional moments of these approximating processes converge to those of the process itself. This result provides us with a new method for estimating the conditional moments, which enables inference in such models. Some numerical examples illustrate the value of the latter approximation in comparison with the more direct representation of the proces obtained from the Cameron‐Martin‐Girsanov formula (see, for example, Brockwell (On continuous time threshold ARMA processes.J. Stat. Planning Inference39 (1994). 291–304) and Brockwell and Stramer (On the approximation of continuous time threshold ARMA processes.Ann. Inst. Statist. Math., to

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00272.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY

摘要:

Abstract.We present a Bayesian approach for estimating nonparametrically an additive autoregressive model with the regression curve estimates cubic smoothing splines. Our approach is robust to innovation outliers; it can handle missing observations and produce multistep ahead forecasts. The computation is carried out using Markov chain Monte Carlo and requires O(nM) operations wherenis the sample size andMis the number of Markov chain iterations. This makes it the first exact algorithm for spline smoothing of an additive autoregressive model which can handle large data sets. The properties of the estimates and forecasts are studied empirically using simulated and real data sets.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1996.tb00273.x

出版商:Blackwell Publishing Ltd    

年代:1996

数据来源: WILEY