Local polynomial Whittle estimation of perturbed fractional processes

We propose a semiparametric local polynomial Whittle with noise estimator of the memory pa- rameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptotic vari- ance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal for d 2 (0; 3=4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, pn. A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical in- vestigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator.