Long Memory Properties and Complex Systems
Figure 17 . Autocorrelation function plots .
more similar to an exponential decay ( but still , being hard to distinguish from a hyperbolical decay ). Moreover , a direct comparison can be made between Figure 16 and the evolution of the mean process . While rules 18 , 110 and 150 display a similar speed of convergence towards to an equilibrium point , rule 106 exhibits a very slow speed of convergence , and rule 182 displays a very fast convergence towards the steady state of the system .
Moreover , it was carried out the V / S and R / S Statistic Tests following the same methodology , as in the previous exercise , in order to detect the presence of long-range dependency .
In the next table , it follows the results for the systems initialized with p 0
= 0.01 :
Table 2 . Acceptance Ratio of Statistic Tests for p 0 = 0.01
Rule
V / S Test Acceptance for Long Memory @ 95 %
R / S Test Acceptance for Long Memory @ 95 %
Rule 18 92 % 88 %
Rule 106 100 % 100 % Rule 110 99 % 91 % Rule 150 99 % 90 % Rule 182 84 % 3 %
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