Improving estimation of the fractionally differencing parameter in the SARFIMA model using tapered periodogram

This paper presents a new method to estimate the fractional differencing parameters in the SARFIMA model. A technique of split cosine bell tapering is suggested to improve the EGPH method. The simulation study shows that the optimal split proportion and bandwidth for the EGPH with split cosine bell tapering method respectively are p = 0.1 and b = 0.9. The new method with the optimal parameters outperforms the EGPH and EGPH with cosine bell tapering. We further applied the EGPH method to estimate intraday volume series and high-frequency absolute return data. The results show that the seasonal fractionally differencing parameters are all estimated to be large, while the nonseasonal fractionally differencing parameters are all very small. This indicates that their long memory property may be mainly caused by the structure of long-range dependence at the seasonal lags instead of dependence at the nonseasonal lags.