SMOOTHED PERIODOGRAM ASYMPTOTICS AND ESTIMATION FOR PROCESSES AND FIELDS WITH POSSIBLE LONG-RANGE DEPENDENCE

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:45

Article

HEYDE, CC ; GAY, R

关键词: CENTRAL LIMIT THEOREM;    ESTIMATING FUNCTION;    ASYMPTOTIC QUASI-LIKELIHOOD;    SMOOTHED PERIODOGRAM;    RANDOM PROCESS;    RANDOM FIELD;    LONG-RANGE DEPENDENCE;   

DOI  :  10.1016/0304-4149(93)90067-E

来源: Elsevier

【 摘 要 】

In this paper we establish central limit theorems for the smoothed unbiased periodogram integral-pi/-pi ... integral-pi/-pi g(omega, theta){I(T,X)*(omega) - EI(T,X)*(omega)} domega1 ... domega(r), where {X(t)} is a stationary r-dimensional random process or random field, possibly with long-range dependence, which is not necessarily Gaussian. Here I(T,X)*(omega) is the unbiased periodogram and g(omega, theta) is a smoothing function satisfying modest regularity conditions. This result implies asymptotic normality of the asymptotic quasi-likelihood estimator of a distributional characteristic theta of the process {X(t)} under very general conditions. In particular, these results show the asymptotic optimality of the Whittle estimation procedure for both short and long-range dependence in the absence of the Gaussian assumption, and extend those of Giraitis and Surgailis (1990) for the case r = 1.

【 授权许可】

Free