  Motivated by the hypothesis that financial crashes are macroscopic examples
of critical phenomena associated with a discrete scaling symmetry, we
reconsider the evidence of log-periodic precursors to financial crashes and
test the prediction that log-periodic oscillations in a financial index are
embedded in the mean function of this index. In particular, we examine the
first differences of the logarithm of the S&P 500 prior to the October 87 crash
and find the log-periodic component of this time series is not statistically
significant if we exclude the last year of data before the crash. We also
examine the claim that two separate mechanisms are responsible for draw downs
in the S&P 500 and find the evidence supporting this claim to be unconvincing.
