For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties are well established. However, except for some specific cases, little is known about the estimation of the...

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 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...

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w is unknown, asymptotic distribution theory for estimates of parameters, including the...

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be inconsistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of Zaffaroni (1999), who established the same...

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...