A new method to analyse the structure function (SF) has been construct
ed and used in the analysis of the AE time series for the years 1978-8
5 and Dst time series for 1957-84. It is shown that this SF analysis m
akes 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 an
alysis, the Dst data are dominated by the 24-hour and 27-day periods.
The 27-day period is modulated by the annual variation.