What is fractional integration?

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.