Fractional Integration and the Business cycle

We show in this article that fractionally integrated univariate models for gdp lead to a better replication of the main business cycle characteristics. We firstly show that the business cycle features are clearly affected by the degree of integration as well as by the other short run (ar, ma, etc.) components of the series. Then, we model the real gdp in the uk and the us by means of fractionally arima (arfima) model, and show that the time series can be specified in terms of this type of model with orders of integration higher than one but smaller than two. Comparing the arfima specifications with those based on arima models, we show via simulations that the former better describe the business cycles features of the data.