Misplaced confidence: limits to statistical inference in cyclostratigraphy

Spectral (frequency-domain) analysis is used for quantitative confirmation of cyclicity in climate-proxy data. Cyclostratigraphic power spectra are typically accompanied by 'confidence limits, whether or not a statistical test has been explicitly invoked. Peaks in spectral power suggest candidate cyclic frequencies; confidence limits (CLs) appear to provide a visual guide to their relative importance, and are conventionally used in a correspondingly informal way. Confidence limits are, however, inseparable from formal tests of statistical significance; they derive from a statistical null hypothesis, and provide a threshold for its acceptance or rejection. In the procedure conventionally used in cyclostratigraphy (and implemented in several specialised software packages), noise models and confidence limits are generated automatically. Although the user may be unaware of it, the null hypothesis on which these CLs are based is calibrated for a (confirmatory) test of significance at exactly one frequency. Extending their application to an exploratory search of spectral peaks at all frequencies is statistically inadmissible. Debate over the role and correct calculation of CLs in cyclostratigraphy remains unresolved: this contribution seeks to clarify the disagreement over their use by explaining the role of CLs in statistical significance tests generally, and comparing it with their conventional use in cyclostratigraphy. Through examples of the correct and incorrect use of the conventional method, I show that the customary informal use of statistical test criteria cannot be sustained. Significance thresholds cannot be calculated in most cases; wrongly estimated confidence limits lead to false positive cycle identifications, with adverse consequences for calibration of the geological time scale.