摘要:

Abstract.This paper deals with three test statistics for a moving‐average (MA) unit root. The spectral test is based on the estimate of the spectral density at frequency zero. The variance difference statistic compares the sample variance of the integrated series with the estimated variance imposing the MA unit root constraint. Furthermore, Tanaka's score type test statistic is modified to improve the power in higher order models. The asymptotic power of the tests is considered and Monte Carlo experiments are performed to investigate the small sample properties of the tests. Finally, the tests are applied to a number of economic time series to determine the degree of integratio

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00199.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.Two alternative methods are considered for identifying what lags to use in a nonlinear model relating a pair of series. One is based on a mutual information function, the other is Kendall's r. They both have the property that if each variable is instantaneously transformed, such that ranks are preserved, then the functions are unchanged. Simulations find properties of the functions and allow application to generated nonlinear series. In simple cases, the methods appear to find frequently the correct lags.

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00200.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.The essence of this paper is the exact evaluation of varSn, whereSnis the number of peaks in a segment ofnreadings from a stationary Gaussian autoregressive moving‐average (ARMA) process, and of the asymptotic normality of (Sn–ESn)/(varSn)1/2. The emphasis is on the AR(1) and MA(1) cases, motivated by Stigler (Estimating serial correlation by visual inspection of diagnostic plots.Am. Statistician40 (1986), 111–16). The evaluation of varSnis based on a discussion of closed‐form calculation of orthant probabilities for a zero mean quadrivariate normal with correlation structure new to the literature. Related issues are the power of the peaks test against stationary alternatives and the good fit of the normal even for smalln.validated by sim

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00201.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.Let (Xi,Yi),i= 0, pL 1,… denote a bivariate stationary time series withXibeing Rd‐valued andYibeing real‐valued. We consider the regression modelYi=θ(Xi) +Zi, where θ(·) is an unknown function and Ziis an autoregressive process. Given a realization of lengthn, we examine the problem of estimating the nonparametric function θ(·) and the parametric componentZi. Under appropriate regularity conditions, it is shown that both components can be optimally

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00202.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY

摘要:

Abstract.We study the problem of non‐parametric spectrum estimation of a stationary time series that might contain periodic components. In this case the periodogram ordinates have a significant amplitude at frequencies near the frequencies of the periodic components. These can be regarded as outliers in an asymptotically exponential sample. We develop a non‐parametric estimator for the spectral density that is insensitive to these outliers in the frequency domain. This is done by robustifying the usual kernel estimator (smoothed periodogram) by means of M‐estimation in the frequency domain. We propose to use data‐tapered periodograms, which yield a drastic improvement of the procedure, typically for the contaminated situation. This is both shown theoretically and supported by means of simulation. We show consistency of the resulting estimator in the general case, and asymptotic normality in the special case of a Gaussian time series, whether contamination is present or not. Finally we illustrate the finite sample performance of the estimating procedure by some simulation results and by application to the Canadian lynx trappin

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1994.tb00203.x

出版商:Blackwell Publishing Ltd    

年代:1994

数据来源: WILEY