Extended Data Fig. 5: Time-series analysis algorithm tests.

a, b, Testing the peak-lag algorithm to detect relationships in a series of surrogate time series with known lags applied. The ‘actual lag’ axes represent the known lag time imposed between pairs of the surrogate series and the ‘calculated lag’ axes show the lag estimated by the algorithm. A perfect performance would manifest as a 1:1 straight line through the scatter points. In b, the violin plots show the mean, median and kernel probability-density estimates of calculated lags from 10⁴ iterations of the test. c, Results of the ‘glacial accumulation’ algorithm with each shaded curve representing IRD_MAR (green) and δ¹⁸O_benthic (purple) integrated and normalized to 100% within each glacial cycle. Above, the δ¹⁸O_benthic record is shown (purple solid line) with green triangles denoting the peak interglacials identified and the dashed black line showing the δ¹⁸O_benthic threshold above which the transitions from glacial to interglacial conditions are defined. d, Gaussian kernel-based cross-correlation (gXCF)⁸⁶ function for AP_comp IRD_MAR versus δ¹³O_benthic and δ¹³C_benthic. The horizontal lines show the 95% Monte Carlo confidence levels for significant cross-correlation.