Nonparametric testing of variability and trend in some climatic records

We use the method of surrogates to test the structure of variability in nine paleoclimate reconstructions and to compare temperature trends with that of the modern temperature record in the Northern hemisphere. Three different algorithms are used to generate surrogate time series: the iterated amplitude adjusted Fourier transform (IAAFT), the statically transformed autoregressive process (STAP) and a modification of STAP, which generates surrogates of arbitrary length (STAPL). We assessed through formal statistical tests that the surrogates preserve the LTP structure of the reconstructed time series of global temperature, using different measures (Hurst exponent, DFA exponent and R/S analysis). Then using the same surrogates we tested for the presence of a linear trend at least as great as the trend of the modern time series against the null hypothesis that the observed trend is only due to LTP. The null hypothesis could be rejected at the lowest possible significance level for all but two of the reconstructions. The result from the non-parametric test adds further statistical evidence to that of earlier parametric studies that the observed global warming trend in the modern time series cannot be adequately explained by natural agents of variability.