摘要:

Abstract.We consider estimation of parameters of an unobservable ARMA(p, q) process {Ut;t= 1,2,…} based on a set ofnobservables,X1, …,Xn, whereXt=Ut, +εt, 1 ≤t≤n, it being assumed that {εt} is independent of {Ut}. We examine the asymptotic properties of these ARMA estimators under a set of weak regularity condition

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00220.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.We consider the asymptotic characteristics of the periodogram ordinates of a fractionally integrated process having memory parameterd≥ 0.5, for which the process is nonstationary, ord≤ ‐.5, for which the process is noninvertible. Series havingdoutside the range (‐.5,.5) may arise in practice when a raw series is modeled without preliminary consideration of the stationarity and invertibility of the series or when a wrong decision is made concerning the stationarity and invertibility of the series. We find that the periodogram of a nonstationary or noninvertible fractionally integrated process at thejth Fourier frequency ωj= 2πj/n, wherenis the sample size, suffers from an asymptotic relative bias which depends onj.We also examine the impact of periodogram bias on the regression estimator ofdproposed by Geweke and Porter‐Hudak (1983) in finite samples. The results indicate that the bias in the periodogram ordinates can strongly affect the GPH estimator even when the number of Fourier frequencies used in the regression is allowed to depend on the length of the series. We find that data tapering and elimination of the first periodogram ordinate in the regression can reduce this bias, at the cost of an increase in variance for nonstationary series. Additionally, we find for nonstationary series that the GPH estimator is more nearly invariant to first‐differencing when a data

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00221.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.A continuous time series is often observed or sampled at discrete intervals. Most literature has dealt with the case when the sampling intervals are equally spaced. For irregularly sampled data, most existing literature is concerned with second‐order moments or anti‐aliasing spectral estimations. We study the estimation of higher‐order spectral density functions with the emphasis on the bispectral estimate when the continuous time series is sampled by a random point process. Estimates under the Poisson sampling scheme are studied in detail. Asymptotic bias and covariances are obtained. In particular, it is shown explicitly how the information of the sampling process comes into play in obtaining a consistent estimate of the bispectral density function of a continuous time series. In contrast to the second‐order spectral density function estimation where the Poisson sampling scheme results in a constant correction term, a consistent bispectral density function estimate results in a nonlinear correction term even in the Poisson sampling scheme. A simple simulation example is presented for illus

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00222.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.The theory of nonparametric spectral density estimation based on an observed stretchX1,…,XNfrom a stationary time series has been studied extensively in recent years. However, the most popular spectral estimators, such as the ones proposed by Bartlett, Daniell, Parzen, Priestley and Tukey, are plagued by the problem of bias, which effectively prohibits ✓N‐convergence of the estimator. This is trueevenin the case where the data are known to bem‐dependent, in which case ✓N‐consistent estimation is possible by a simple plug‐in method.In this report, an intuitive method for the reduction in the bias of a nonparametric spectral estimator is presented. In fact, applying the proposed methodology to Bartlett's estimator results in bias‐corrected estimators that are related to kernel estimators with lag‐windows of trapezoidal shape. The asymptotic performance (bias, variance, rate of convergence) of the proposed estimators is investigated; in particular, it is found that the trapezoidal lag‐window spectral estimator is ✓N‐consistent in the case of moving‐average processes, and ✓(N/log/N)‐consistent in the case of autoregressive moving‐average processes. The finite‐sample performance of the trapezoidal lag‐window estimator is also assessed

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00223.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.We treat a problem of estimating unknown coefficients of a time series regression when the variance of the error changes with time, i.e. when a process which the error term obeys is nonstationary. First, we show the weak consistency of the ordinary least squares estimator for the coefficients of a polynomial regression under some assumptions on the covariance structure of the error process. Next, we propose a nonparametric method for estimating the variance of the error process and a weighted least squares estimator of the regression coefficients, which is constructed by using the estimator of the variance. We investigate statistical properties of our proposed estimator in the following way. We consider the prediction of a future value of a linear trend by using our proposed estimator and evaluate its prediction error. By simulation studies, we compare the prediction error of the predictor constructed by using our proposed estimator with the prediction errors obtained for other estimators including the ordinary least squares estimator when the variance of the error process increases with time and the sample sizes are small. As a result, our proposed estimator seems to be reasonable.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00224.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.Two‐stage estimators have been proposed in fractional autoregressive integrated moving‐average (ARIMA) systems which first estimate the long‐run features of the system semi‐parametrically and then estimate the short‐run features by usual methods in a second stage. Although asymptotic theory is available for the estimates in the first stage of such a procedure, we are aware of no results concerning the estimates in the second stage. In this paper we provide a stochastic order of magnitude associated with an estimator in this class and discuss th

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00225.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY