Testing the existence of multiple cycles in financial and economic time series

In this article we show that multiple cycles can occur in financial and economic time series. We model these cycles by means of Gegenbauer processes, using a procedure that permits us to test multiple roots at fixed frequencies over time. and thus, it permits us to approximate the length of each cycle. This procedure is applied to one economic time series (US monthly unemployment rate) and a financial one (US Federal Funds rate of interest), and the results show that both series can be specified in terms of a multiple cyclical fractional model.