摘要:

Abstract.The inverse correlation function of a stationary time series was introduced by Cleveland (The inverse autocorrelations of a time series and their applications.Technometrics14 (1972), 277–93). In this paper inverse correlations are defined for non‐stationary time series {xt, integert} such thatyt= (1 —Bs)dxtis second‐order stationary. The linear interpolator and the inverse process of {xt} are also defined:their weights are shown to be time invariant and proportional to the inverse correlations. The interpolation method for the estimation of the inverse correlation function of a stationary time series is extended to the non‐stationary series {xt} and the asymptotic properties of the estimates are found to be similar to those in the statio

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00252.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.In this paper I reconsider two of the questions raised by Granger and Hallman (Nonlinear transformations of integrated time series.J. Time Ser. Anal.12 (1991), 207–24):(i) IfXtis I(1) andZt=h(Xt), isZtalso I(1)? (ii) CanXtandh(Xt) be cointegrated? The distinction between I(1) and I(0) processes is replaced by the distinction between long memory and short memory processes, where for short memory I mean strong mixing. By exploiting the fact that random walks (with positive trend component) are martingales (submartingales) and are also first‐order Markov, I show that (a) unbounded convex (concave) and strictly monotonic transformations of random walks are always long memory processes, (b) polynomial, strictly convex (concave) transformations of random walks display a unit root component, but the first differences of such transformations need not be short memory, and (c)Xtandh(Xt), withhan unbounded convex (concave) or strictly monotonic function, can never be cointegra

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00253.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.The inverse of the covariance matrix of a moving‐average process of general order is considered. A recursive relationship between the inverses for any two consecutive orders has been established. Illustrative situations are derived and exact expressions are discusse

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00254.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.Hall (Testing for a unit root in the presence of moving average errors.Biometrika76 (1989), 49–56; Joint hypothesis tests for a random walk based on instrumental variable estimators.J. Time Ser. Anal.13 (1992), 29–45), Pantula and Hall (Testing for unit roots in autoregressive moving average models:an instrumental variable approach.J. Econometrics48 (1991), 325–53) and Lee and Schmidt (Unit root tests based on instrumental variable estimation.Int. Econ. Rev.39 (1994), 449–62) proposed instrumental variable (IV) based tests for a unit root in an ARMA(p+ 1,q) time series. To perform the tests it is essentially necessary to know (p,q) but in many cases this information is unknown. In practice a natural solution to this problem is to estimate (p,q) from the data using a strategy based on the residual autocovariances from the IV regression. In this paper we examine the properties of these residual autocovariances under various assumptions about the true nature of the time series. This analysis allows us to propose a model selection procedure which has desirable asymptotic and finite sample properties whether the time series is stationary or possesses a unit root. A sideproduct of our analysis is that we extend Box and Pierce's (Distribution of residual autocorrelations in autoregressive integrated moving average time series models.J. Am. Statist. Assoc.65 (1970), 1509–26) analysis of the least squares residual autocorrelations to the residual autocovariances from IV re

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00255.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.A stochastic sequence generated by a chaotic map has extremely strong dependence in a structural sense, in that any data value may be represented exactly as a known deterministic function of any one of its antecedents. However, the range of dependence of the time series may be very short in a statistical sense ‐ in fact, all its lagged correlations could be zero. In the present paper we study the implications of this property for two of the statistical techniques which weak dependence is often invoked to justify ‐ asymptotic methods based on the central limit theorem, and the bootstrap. It is shown that in the case of the logistic map, the validity of these techniques depends critically on the value of the parameter governing the map. Very small alterations to the parameter value can produce dramatic changes in the strength of dependence, thereby altering the validity of even elementary statistical procedures based on asymptotic normality or resampl

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00256.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.In this paper we investigate the merits of using a data taper in non‐linear functional of the periodogram of a stationary time series. To this end, we show consistency for a general class of statistics of the form, where A(ω) is a function of bounded variation and where φ is allowed to be a non‐linear function of the periodogramIT(ω) of thetapereddata. The key step in deriving our asymptotic results is an Edgeworth expansion for the finite Fourier transform of the tapered data, which do not have to follow a particular distribution (i.e. we allow for non‐Gaussianity). Important applications are the estimation of, choosing φ to be a suitable transform of a given functiong(see Taniguchi, On estimation of the integrals of certain functions of spectral density.J. Appl. Prob.17 (1980). 73–83), the peak‐insensitive spectrum estimator of von Sachs (Peak‐insensitive nonparametric spectrum estimation.J. Time Ser. Anal.15 (1994), 429–52), where φ is chosen to be a bounded (robustifying) σ function, and the parametric approach of Chiu (Peak‐insensitive parametric spectrum estimation.Stoch. Proc. Appl.35 (1990). 121–40) on robust estimation of the parameters of the continuous spec

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00257.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.The purpose of this paper is to complement the theory of exact maximum likelihood estimation in pure autoregressive processes by differentiating the exact Gaussian likelihood function with respect to the model parameters and obtaining a set of likelihood equations very similar in form to the Yule—Walker equations. The main contribution of this paper is a very simple expression for the derivatives and the resulting likelihood equations in terms of the components of a (p+ 1) x (p+ 1) function of the data, the model parameters (s̀2,φ) and the autocovariances at lags 0 throughp.We propose an iterative algorithm for solving the likelihood equations by alternately solving two linear systems, first for (s̀2,φ) given current estimates of the autocovariances, then for updated estimates of the autocovariances given current estimates of (s̀2,φ). The number of operations per iteration is independent of the series length since the algorithm uses the data only through the value of the (p+ 1) x (p+ 1) sufficient st

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00258.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

摘要:

Abstract.This paper investigates theoretical aspects of the relationship between the generalized least squares and Gaussian estimation schemes for vector autoregressive moving‐average models. The asymptotic convergence of the generalized least squares estimator to the Gaussian estimator is established and an alternative numerical method for implementing the generalized least squares scheme is proposed. Finally, some simulation results are presented to illustrate the theor

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00259.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY

ISSN:0143-9782    

DOI:10.1111/j.1467-9892.1995.tb00260.x

出版商:Blackwell Publishing Ltd    

年代:1995

数据来源: WILEY