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, which are useful in statistical inference on index models. They were shown to be asymptotically normal under weak dependence conditions by Robinson (1989) and under serial independence by Powell et al. (1989). We find that an element of long-range dependence can lead either to a nonnormal limiting distribution, or else to a normal one with a limiting variance which differs from that which obtains in case of weak dependence, implying that inferences incorrectly based on weak-dependence assumptions will be invalid.