This paper considers a class of semiparametric models being the sum of a non-parametric trend function g and a FARIMA-GARCH error process. Estimation of ĝ (v), the vth derivative of g, by local polynomial fitting is investigated. The focus is on the derivation of the asymptotic normality of ĝ...

Filtered log-periodogram regression estimation of the fractional differencing parameter d is considered. Asymptotic properties are derived and the effect of filtering on ˆd is investigated. It is shown that the estimator by Geweke and Porter-Hudak (1983) can be improved significantly using a...