Publication Date: August 2002
This paper determines coverage probability errors of both delta method and parametric bootstrap conﬁdence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d0 are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The ﬁrst estimator solves the ﬁrst-order conditions with respect to the covariance parameters of a “plug-in” log-likelihood function that has the unknown mean replaced by the sample mean. The second estimator does likewise for a plug-in Whittle log-likelihood.
The magnitudes of the coverage probability errors for one-sided bootstrap CIs for covariance parameters for long-memory time series are shown to be essentially the same as they are with iid data. This occurs even though the mean of the time series cannot be estimated at the usual n1/2 rate.
Asymptotics, conﬁdence intervals, delta method, Edgeworth expansion, Gaussian process, long memory, maximum likelihood estimator, parametric bootstrap, t statistic, Whittle likelihood
JEL Classification Codes: C12, C13, C15
Published in Journal of Econometrics (2006), 133(2): 673-702 [DOI]