The most striking conclusion of this paper is that measuring the Hurst parameter, even
in artificial data, is very hit and miss.
Figure 3: (a) Southern Oscillation Index (SOI) data (black) versus
artificial data proportional to the SOI, and with normally - distributed white noise and a sinusoidal signal added (red).
Can you show us the effect Zach refers to with
some artificial data (decreasing noise amplitude with time)?
In fact, if you plug
an artificial data series with a long - term trend in it, that trend gets wiped out completely, leaving just shorter term variability behind.
Even leaving aside the fact that he failed to correct the SAC in his own regressions on the GISS - E data, I don't understand how he could claim that he demonstrated our results are spurious when he could not replicate them on
his artificial data set.