Unconditional mean, Volatility and the Fourier-Garch representation

This paper proposes a new model called Fourier-GARCH that is a modification of the popular GARCH(1,1). This modification allows for time-varying first and second moments via means of Flexible Fourier transforms. A nice feature of this model is its ability to capture both short and long run dynamics in the volatility of the data, requiring only that the proper frequencies of the Fourier transform be specified. Several simulations show the ability of the Fourier series to approximate breaks of an unknown form, irrespective of the time or location of breaks. The paper shows that the main cause of the long run memory effect seen in stock returns is the result of a time varying first moment. In addition, the study suggests that allowing only the second moment to vary over time is not sufficient to capture the high persistence observed in lagged returns.