Journal on Policy and Complex Systems
Figure 5 . Simulated prices over time .
With a probability q = 0.5 of having a positive or negative external information , according to the mentioned Bernoulli variable , the system converges rapidly towards a high-level or a low-level price . In the case of Figure 5 , it converged towards a high-level price .
Having estimated the fractional difference coefficients , it was obtained an average Künsch ( 1987 ) estimate of 0.3211652 , while the average GPH ( Geweke & Porter-Hudak , 1983 ) estimate was 0.06440041 .
Again , if taken into account the fact that the past state is Boolean and the autoregressive part of the function is still weak ( less than 0.9 ), the GPH results provide weak evidences towards the presence of long memory components in this kind of process — in this case , it suggests a White Noise Process . On the other hand , the Künsch ( 1987 ) estimates provide evidences towards the presence of these long-range dependencies .
The distribution of the fractional difference estimates ( GPH ) is described in Figure 6 .
In contrast to the previous distribution , in Figure 6 is clear that this process does not exhibit long memory properties . In Figure 7 , it is shown the distribution of the fractional difference coefficient estimates according to Künsch ( 1987 ).
When analyzing Figure 7 it is important to notice that its shape is completely different from those obtained in the previous cases . This distribution suggests the presence of a long-range
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