We discuss some inference problems associated with the fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>H</mi> </math> </EquationSource> </InlineEquation> is known and is in <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation>

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be...