Recent results on so-called SEMIFAR models introduced by Beran (1997) are discussed. The nonparametric deterministic trend is estimated by a kernel method. The differencing and fractional differencing parameters as well as the autoregressive coefficients are estimated by an approximate maximum...

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