A new method to analyse the structure function (SF) has been constructed and used in the analysis of the AE time series for the years 1978--85 and Dst time series for 1957--84. It is shown that this SF analysis makes a clear distinction between affine and periodicity dominated time series, and it displays the essential periodicities of the series in a range relevant to its characteristic time scale. The AE time series is found to be affine such that the scaling exponent changes at a time scale of 113 (¿9) minutes. On the other hand, in the SF function analysis, the Dst data are dominated by the 24-hour and 27-day periods. The 27-day period is modulated by the annual variation. ¿ American Geophysical Union 1995