  We show that log-periodic power-law (LPPL) functions are intrinsically very
hard to fit to time series. This comes from their sloppiness, the squared
residuals depending very much on some combinations of parameters and very
little on other ones. The time of singularity that is supposed to give an
estimate of the day of the crash belongs to the latter category. We discuss in
detail why and how the fitting procedure must take into account the sloppy
nature of this kind of model. We then test the reliability of LPPLs on
synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even
this case is borderline regarding predictability of divergence time. We finally
argue that current methods used to estimate a probabilistic time window for the
divergence time are likely to be over-optimistic.
