Journal on Policy and Complex Systems
Keeping in mind such stochastic properties observed in the second configuration , the GPH ( Geweke & Porter-Hudak , 1983 ) procedure was performed in order to analyze the long memory properties of such process and it was obtained the distribution presented in Figure 21 , over 100 different experiments .
Figure 21 . Histogram of the parameter d .
As can be seen in Figure 21 , there is a strong evidence of the presence of long-range dependency in the analyzed stochastic process . In this specific case , the mean of this distribution is 0.8418075 and its standard deviation is 0.02211333 . It is also important to mention that the Künsch ( 1987 ) procedure failed in the R package and consequently did not produce any result that could be shown in this paper .
Additionally , it is also important to notice that the autocorrelation function decays very slowly over the time , as can be seen in Figure 22 .
Furthermore , both V / S and R / S Statistic Tests point out that all of the 100 generated samples have long-range dependency , at a 95 % confidence level . Hence , there is no doubt that long memory behavior emerges in this case .
Therefore , from the case analyzed along this section , it is possible to show that spatial complexity plays a major role in the rise of long memory properties , when setting all agents behavior homogeneously and avoiding direct local interactions between themselves — in order to try to avoid all factors discussed previously .
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