Tests and confidence intervals for the location parameter in orthogonal FEXP models

Confidence intervals and tests for the location parameter are considered for time series generated by FEXP models. Since these tests mainly depend on the unknown fractional differencing parameter d, the distribution of d plays a major role. An exact closed form expression for the asymptotic variance of d is given for FEXP models with cosine functions. It is shown that the variance increases linearily with the order p of the model. An alternative FEXP model with orthogonal components is proposed for which the asymptotic variance of d does not depend on p. Tables of quantiles of the test statistic are given for both model classes.