** **Working
Paper 99-01

Department of Economics

University of North Carolina, Chapel Hill

http://www.unc.edu/depts/econ

** What is Fractional Integration?**

William R. Parke

June 8, 1999

Abstract

A simple construction that will be referred to as an error duration model is shown to generate fractional integration and long memory. An error duration representation also exists for many familiar ARMA models, making error duration an alternative to autoregression for explaining dynamic persistence in economic variables. The results lead to a straightforward procedure for simulating fractional integration and establish a connection between fractional integration and common notions of structural change. Two examples show how the error duration model could account for fractional integration in aggregate employment and in asset price volatility.

keywords: fractional integration, long memory, error duration model, structural change, simulation.