We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T logT . For moderate and large sample sizes, the difference in computation time is substantial.
Journal of Time Series Analysis, 2014, Vol 35, Issue 5, p. 428-436
Circular convolution theorem; Fast Fourier transform; Fractional difference