A fast fractional difference algorithm - Andreas Noack Jensen; Morten Ørregaard Nielsen (Queen's University, Department of Economics, 2013)
We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (complexity) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log2 T . For moderate and large sample sizes, the difference in computation time is substantial.
Keywords: C22; C63; C87; 330; Circular convolution theorem; fast Fourier transform; fractional difference