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

Spectral analysis of the Greenland Ice Sheet Project 2 (GISP2) delta O-18 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 H-0 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 delta O-18 structure, whereas higher-order ARMA processes result in approximately level spectral estimates. After suitably leveling GISP2 d 18O 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.

Automated summary

Spectral analysis of the GISP2 delta O-18 record revealed a 1/(1470 yr) peak, which was later found to be insignificant after adjustments and multiple hypothesis testing. The study highlights the importance of considering higher-order ARMA processes in evaluating spectral significance.