A Recursive Algorithm For Fractionally Differencing Long Data Series

Abstract

We propose a recursive algorithm to fractionally difference time series data. The algorithm eliminates the need to evaluate the gamma function directly, and hence avoids the overflow problem that arises when fractionally differencing a long data series. The proposed algorithm can be implemented using any general matrix programming language. An implementation using SAS is presented. The algorithm and the code provide a practical approach to including fractional differencing as part of a time series data analysis.