Flexible Seasonal Long Memory and Economic Time Series

We discuss specification, frequency domain estimation and application of flexible fractionally integrated seasonal long memory time series models, which allow for 'chi-squared' (seasonal) unit root testing. We suggest periodogram regression and approximate ML estimation. We successfully apply a flexible model on post war US GNP data, which shows the statistical significance of seasonal 'overdifferencing' 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.