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The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order m-1/2 (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild

Topics:
HA Statistics

Year: 2003

DOI identifier: 10.1214/aos

OAI identifier:
oai:eprints.lse.ac.uk:291

Provided by:
LSE Research Online

Download PDF:- (2000). A Bias-Reduced Log-Periodogram Regression Estimator for the Long-Memory Parameter. Preprint, Cowles Foundations for Research in Economics,
- (2000). Adaptive semiparametric estimation of the memory parameter.
- (1972). An asymptotic expansion for the distribution of a statistic admitting an asymptotic expansion.
- (2000). An ecient taper for potentially overdierenced longmemory time series.
- (1996). Bandwidth choice in Gaussian semiparametric estimation of long-range dependence, in:
- (1999). Broad band log-periodogram regression of time series with long range dependence.
- (2001). Broadband semiparametric estimation of the memory parameter of a long-memory time series using fractional exponential model.
- (1982). Determining the degree of dierencing for time series via log spectrum. J.Time Series Anal.
- (1991). Edgeworth expansions for nonparametric density estimators, with applications.
- (2000). Edgeworth expansions for semiparametric averaged derivatives.
- (2001). Edgeworth expansions for spectral density estimates and studentized sample mean.
- (1995). Estimation of the memory parameter for nonstationary or noninvertable fractionally integrated processes.
- (1995). Gaussian semiparametric estimation of long range dependence.
- (1999). Gaussian semiparametric estimation of non - stationary time series.
- (1991). Higher Order Asymptotic Theory for Time Series Analysis.
- (2001). Higher-order kernel M -estimation of long memory.
- (1986). Large-sample properties of parameter estimates for strongly depndentstationary Gaussian time series.
- (2001). Local polynomial Whittle estimation of long-range dependence.
- (1995). Log-periodogram regression of time series with long range dependence Ann.
- (1999). Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels.
- (1999). Non-stationary log-periodogram regression.
- (1976). Normal Approximation and Asymptotic Expansions.
- (1982). On the distribution of some statistical estimates of spectral density.
- (1978). On the validity of the formal Edgeworth expansion.
- (1997). Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long range dependence.
- (1987). Statistical aspects of self-similar processes, in
- (1981). Statistical Estimation. Asymptotic Theory.
- (1995). The approximate distribution of nonparametric regression estimates.
- (1973). The asymptotic theory of linear time series models.
- (1983). The estimation and application of long-memo time series models. J.Time Series Anal.
- (1975). Time Series: Data Analysis and Theory. Holden Day,
- (2001). Valid Edgeworth expansion for the sample autocorrelation function under long range dependence.

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