Putting the Significance of Spectral Peaks on the Level: Implications for the 1470-Yr Peak in Greenland δ18O

Abstract

Abstract Spectral analysis of the Greenland Ice Sheet Project 2 (GISP2) δ18O record has been interpreted to show a 1/(1470 yr) spectral peak that is highly statistically significant (p < 0.01). The presence of such a peak, if accurate, provides an important clue about the mechanisms controlling glacial climate. As is standard, however, statistical significance was judged relative to a null model, H0, consisting of an autoregressive order one process, AR(1). In this study, H0 is generalized using an autoregressive moving-average process, ARMA(p, q). A rule of thumb is proposed for evaluating the adequacy of H0 involving comparing the expected and observed variances of the logarithm of a spectral estimate, which are generally consistent insomuch as removal of the ARMA structure from a time series results in an approximately level spectral estimate. An AR(1), or ARMA(1, 0), process is shown to be an inadequate representation of the GISP2 δ18O structure, whereas higher-order ARMA processes result in approximately level spectral estimates. After suitably leveling GISP2 δ18O and accounting for multiple hypothesis testing, multitaper spectral estimation indicates that the 1/(1470 yr) peak is insignificant. The seeming prominence of the 1/(1470 yr) peak is explained as the result of evaluating a spectrum involving higher-order ARMA structure and the peak having been selected on the basis of its seeming anomalous. The proposed technique for evaluating the significance of spectral peaks is also applicable to other geophysical records. Significance Statement A suitable null hypothesis is necessary for obtaining accurate test results, but a means for evaluating the adequacy of a null hypothesis for a spectral peak has been lacking. A generalized null model is presented in the form of an autoregressive, moving-average process whose adequacy can be gauged by comparing the observed and expected variance of log spectral density. Application of the method to the GISP2 δ18O record indicates that spectral structure found at 1/(1470 yr) is statistically insignificant.