SEMIPARAMETRIC ESTIMATION FROM TIME-SERIES WITH LONG-RANGE DEPENDENCE

This paper studies the behaviour, in the presence of long-memory time- series dependence, of semiparametric averaged derivative statistics, w hich are useful in statistical inference on index models. They were sh own to be asymptotically normal under weak dependence conditions by Ro binson (1989) and under serial independence by Powell et al. (1989). W e find that an element of long-range dependence can lead either to a n onnormal limiting distribution, or else to a normal one with a limitin g variance which differs from that which obtains in case of weak depen dence, implying that inferences incorrectly based on weak-dependence a ssumptions will be invalid.