GAUSSIAN SEMIPARAMETRIC ESTIMATION OF LONG-RANGE DEPENDENCE

Assuming the model f(lambda) similar to G lambda(1-2H), as lambda --> O +, for the spectral density of a covariance stationary process, we c onsider an estimate of H is an element of (0, 1) which maximizes an ap proximate form of frequency domain Gaussian likelihood, where discrete averaging is carried out over a neighbourhood of zero frequency which degenerates slowly to zero as sample size tends to infinity. The esti mate has several advantages. It is shown to be consistent under mild c onditions. Under conditions which are not greatly stronger, it is show n to be asymptotically normal and more efficient than previous estimat es. Gaussianity is nowhere assumed in the asymptotic theory, the limit ing normal distribution is of very simple form, involving a variance w hich is not dependent on unknown parameters, and the theory covers sim ultaneously the cases f(lambda) --> infinity, f(lambda) --> 0 and f(la mbda) --> C is an element of (0, infinity), as lambda --> 0. Monte Car lo evidence on finite-sample performance is reported, along with an ap plication to a historical series of minimum levels of the River Nile.