  The interaction between the Earth's magnetic field and the solar wind plasma
results in a natural plasma confinement system which stores energy. Dissipation
of this energy through Joule heating in the ionosphere can be studied via the
  Auroral Electrojet (AE) index. The apparent broken power law form of the
frequency spectrum of this index has motivated investigation of whether it can
be described as fractal coloured noise. One frequently-applied test for
self-affinity is to demonstrate linear scaling of the logarithm of the
structure function of a time series with the logarithm of the dilation factor
$\lambda$. We point out that, while this is conclusive when applied to signals
that are self-affine over many decades in $\lambda$, such as Brownian motion,
the slope deviates from exact linearity and the conclusions become ambiguous
when the test is used over shorter ranges of $\lambda$. We demonstrate that non
self-affine time series made up of random pulses can show near-linear scaling
over a finite dynamic range such that they could be misinterpreted as being
self-affine. In particular we show that pulses with functional forms such as
those identified by Weimer within the $AL$ index, from which $AE$ is partly
derived, will exhibit nearly linear scaling over ranges similar to those
previously shown for $AE$ and $AL$. The value of the slope, related to the
Hurst exponent for a self-affine fractal, seems to be a more robust
discriminator for fractality, if other information is available.
