A Fast Fractional Difference Algorithm

11 Pages Posted: 7 Jun 2013

See all articles by Andreas Jensen

Andreas Jensen

University of Copenhagen

Morten Ørregaard Nielsen

Queen's University - Department of Economics

Date Written: May 24, 2013

Abstract

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 log T. For moderate and large sample sizes, the difference in computation time is substantial.

Keywords: Circular convolution theorem, fast Fourier transform, fractional difference

JEL Classification: C22, C63, C87

Suggested Citation

Jensen, Andreas and Nielsen, Morten Orregaard, A Fast Fractional Difference Algorithm (May 24, 2013). Available at SSRN: https://ssrn.com/abstract=2269814 or http://dx.doi.org/10.2139/ssrn.2269814

Andreas Jensen

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165
Denmark

Morten Orregaard Nielsen (Contact Author)

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario
Canada

HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/

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