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...

Parametric estimation is discussed in a variety of models exhibiting longrange dependence

We consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of past values of the observable sequence, with square summable weights. This...

The aggregation procedure when a sample of length N is divided into blocks of length m = o(N), m ® ¥ and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu, Teverovsky and Willinger (1995), Teverovsky and Taqqu (1997) introduced an...

For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence rt is the square of an inhomogeneous linear combination of rs, s < t, we give conditions under which, for integers 1 > 2, r' has long memory autocorrelation and normalized partial sums of ri converge to fractional...</t,>