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 the index (conditional upon no crash having yet occurred). In particular, we examine the first differences of the logarithm of the S&P 500 prior to the October 1987 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 needed to explain the frequency distribution of draw downs in the S&P 500 and find the evidence supporting this claim to be unconvincing.
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