Effect of the order of fractional integration on impulse responses

For a fractional time series model integrated of order d we derive two results. First, it is obtained how a change in d affects the coefficients of the integration filter. For long memory (d>0), the effect is always positive; in the case of anti-persistence (d<0) the effect may be positive or negative depending on d. Second, those results are extended to the sequence of autocorrelations for fractionally integrated noise.