Log-periodicity: Fact or fiction?

Abstract

A common empirical practice in LPPLS applications is to calibrate the model under parameter bounds and then declare an “LPPLS signature” when ADF/PP tests on calibration residuals reject a unit root at conventional tabulated critical values. We show that this procedure exhibits substantial size distortion. Using synthetic series that preserve the roughness and volatility of financial data while excluding log-periodic structure, we compute bootstrap critical values by re-estimating the full two-stage procedure on each synthetic sample. Applied to S&P 500 monthly and daily data, conventional thresholds yield inflated rejection rates. In contrast, the bootstrap restores empirical size to nominal levels and overturns many purported signatures. These findings highlight the need for estimation-aligned inference in LPPLS diagnostics and call for a re-examination of published LPPLS evidence that may reflect size-induced false positives.