摘要:

Abstract.Cubic splines and indicator functions are used to estimate the spectral density function and line spectrum, respectively, for a stationary time series. A fully automatic procedure involving maximum likelihood, stepwise addition and deletion of basis functions, and the Bayes information criterion (BIC) is used to select the final model.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00240.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.The logarithm of the spectral density function for a stationary process is approximated by polynomial splines. The approximation is chosen to maximize the expected log‐likelihood based on the asymptotic properties of the periodogram. Estimates of this approximation are shown to possess the usual nonparametric rate of convergence when the number of knots suitably increases to infinit

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00241.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.The variance ratio test is often used as a check of the hypothesis that a time series is generated by a random walk. A natural extension of the test is developed to cover the case where the assumed model is ARIMA(p, 1,q), with unknown parameters. Small sample properties of the generalized test are investigated, and the test is applied to a frequently analysed data set on US quarterly real gross national product. In effect, we are testing for low frequency misspecification in assumed autoregressive moving‐average (ARMA) models for a differenced serie

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00242.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.We compare several estimators for the second‐order autoregressive process and compare the associated tests for a unit root. Monte Carlo results are reported for the ordinary least squares estimator, the simple symmetric least squares estimator and the weighted symmetric least squares estimator. The weighted symmetric least squares estimator of the autoregressive parameters generally has smaller mean square error than that of the ordinary least squares estimator, particularly when one root is close to one in absolute value. For the second‐order model with known zero intercept, the one‐sided ordinary least squares test for a unit root is more powerful than the symmetric tests. For the model with an estimated intercept, the one‐sided weighted symmetric least squares test is the most powerf

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00243.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.The vector autoregressive moving average model with nonlinear parametric restrictions is considered. A simple and easy‐to‐compute Newton‐Raphson estimator is proposed that approximates the restricted maximum likelihood estimator which takes full advantage of the information contained in the restrictions. In the case when there are no parametric restrictions, our Newton‐Raphson estimator is equivalent to the estimator proposed by Reinselet al.(Maximum likelihood estimators in the multivariate autoregressive moving‐average model from a generalized least squares view point.J. Time Ser. Anal.13 (1992), 133–45). The Newton‐Raphson estimation procedure also extends to the vector ARMAX model. Application of our Newton‐Raphson estimation method in rotational sampling problems is discussed. Simulation results are presented for two different restricted models to illustrate the estimation procedure and compare its performance with that of two alternative procedures that ignore the parametr

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00244.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY