Journal on Policy and Complex Systems
If , the model becomes a pure random-walk process ( an ARIMA ( 0,1,0 ) model ).
Figure 1 . Spurious estimates of d versus true AR ( 1 ) coefficient values .
As can be seen in Figure 1 , only high positive values of the autoregressive coefficient can produce potential spurious results in terms of the estimate of the fractional difference coefficients . Still , these spurious effects are not significantly large . The main explanation for such occurrence is the fact that as n , the model becomes more similar to a random-walk process . Hence , in terms of inference of d , it should approximate to 1 .
Furthermore , it is also important to mention that both statistical tests produced the same results for sufficient long series , in this case , 2,000 observations , and the results did not change if a constant was included .
In order to complement this first analysis , it was simulated a case where m , resulting in . Hence , it is possible to conclude that there is an exponential decay behavior in terms of a spurious fractional difference parameter estimate versus the AR ( 1 ) coefficient value .
Hence , only first-order autoregressive processes with an AR coefficient close to 1 ( larger than 0.9 ) can lead to possible distortions in the inference of the fractional difference coefficient , which is something that must be taken into account when evaluating data generating processes .
It is also important to explain how the Modified R / S Statistic ( as in Lo ,
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