Flexible seasonal long memory and economic time series

We discuss speci cation, frequency domain estimation and application of a exible seasonal long memory time series model based on fractional di erencing. This type of model lends itself to seasonal unit root testing using standard distribution theory with null hypotheses of stationarity and nonstationarity. We apply Wald tests. We suggest periodogram regression estimation for simple models, which we evaluate positively using simulation. We apply the exible model on widely used quarterly US GNP data. Approximate ML estimation shows the statistical signi cance of seasonal \overdi erencing" due to seasonal adjustment. Application to monthly shipping data for the Sound (1557-1783) shows the order of integration at frequency 0 and 1/12 about 0.5, with lower values at other frequencies. We use several graphical techniques to evaluate the estimation results in the frequency domain.