Long Memory Properties and Complex Systems
dependency in the analyzed stochastic process .
Another interesting fact is that the shape of the simulated price distribution is completely different in both cases , as seen in Figure 8 .
In Figure 8 , that synthesizes the distribution of the prices in the first case , it can be seen that the prices are very far from a normal distribution , with considerable high fat fails , asymmetry and so on , resembling a Power
Law-like distribution .
Except for the percentile between 0.2 and 0.3 , which has a very strong peak , there is a typical exponential decay , which is one of the most important features in a Power Law distribution .
Furthermore , the characterization of such behavior is very important , because this is one of the most notorious aspects present in self-similar processes , which are naturally one of the emergent properties of complex systems .
Figure 6 . Histogram of parameter d .
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