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...

The distinction between stationarity, difference stationarity, deterministictrends as well as between short- and long-range dependence has a major impact onstatistical conclusions, such as confidence intervals for population quantities or point and interval forecasts. SEMIFAR models introduced...

A class of semiparametric fractional autoregressive GARCH models (SEMIFAR-GARCH), which includes deterministic trends, difference stationarity and stationarity with short-and long-range dependence, and heteroskedastic model errors, is very powerful for modelling ?nancial time series. This paper...

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...