“…of the fit residuals, there is another diagnostic for the bad quality of Model 1: the three different contributions (LPPL, VIX and interest rate r(t)) are large compared with their sum, suggesting the existence of spurious (in the sense of "over-fitting") compensations between these terms. In contrast, since the LPPL term was shown to fit very well the data over the period from 2000 to 2003 [25,26,28,30], the LPPL term should be the leading contribution while the other factors should have been perturbations, perhaps growing with time. In other words, Model 1 is not a perturbation of the LPPL model used previously in [25,26,28,30].…”