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Figure 88 Left: Plot of the different moments among the aggregation scale. A delta value of 100
corresponds to the whole aggregated time series. The smallest value of delta corresponds to 2 minutes
aggregation Right: the behaviour of the exponent tau(q) among the different order of moments q.
This example is not very good because it considers the extended long memory event. It is
indeed not sure that the use of this short data set is relevant. On the contrary, it seems to be
rather a “strange” data set, looking at the obtained behaviour of the exponent tau(q) among
the different order of moment. Indeed, in the most data set presenting multi scaling, the
“observation points” were rather above the straight line. Computing this graph could thus
maybe provide a kind of control about the validity of the used data set. Other indications
about the validity could surely be found analyzing the autocorrelation function. The small
data sets tend to often present some negative autocorrelation after a defined number of lags.
Such patterns are probably not to find in longer data sets.
In closing, it would also probably be interesting to assess if all the different moments present
an inner, a transition and a scaling regime. Moreover, it would be probably indispensable to
check that the aggregation scales at which these different regimes appear are always located at
the same place for the all different moments and that the observed changes are similar.
Otherwise, if the multi scaling is assessed only thanks to parameters that take into account the
behaviour of the tau(q) exponents, it could maybe lead to supplementary extrapolation errors.
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