Fast computation and practical use of amplitudes at non-Fourier frequencies

Abstract In this paper, it is shown that the performance of various frequency-domain estimators memory parameter can be boosted by inclusion non-Fourier frequencies in addition to regular Fourier frequencies. A fast two-stage algorithm for efficient computation amplitudes at these additional presented. first stage, naïve sine and cosine transforms are computed with a modified version Fast Transform. second amended taking violation standard orthogonality conditions into account. considerable number auxiliary quantities, which required do not depend on data therefore only need once. The superior (in terms root-mean-square error) based also demonstrated extensive simulations. Finally, empirical results obtained applying financial high-frequency show significant long-range dependence present absolute intraday returns but signed returns.