Fractional Cyclical Structures & Business Cycles in the Specification of the US Real Output

The issue in this paper is to analyse the business cycle frequencies in the US real output. However, instead of using classical approaches based on linear and non-linear models, we use a specification of fractional cyclical integration, which is based on Gegenbauer processes. We apply a procedure that permits us to test roots with integer and fractional orders of integration at fixed frequencies over time and thus, it permits us to approximate the length of the cycles. The results, based on the first differenced data, show that the cycles have a duration of about four years and a half, with an order of integration higher than 0 but smaller than 0.5, being thus stationary but with a component of long memory behaviour. Comparing this model with those based on ARIMA (and ARFIMA) models, we show via simulations that the fractional cyclical structure can better describe the business cycle features of the data.