Jackknife Tests for Differences in Autocorrelation between Climate Time Series

Abstract

Two tests for differences in the lag 1 autocorrelation coefficient based on jackknife estimates are proposed. These tests are developed for the pooled sample of all daily values in a certain calendar mouth (e.g., all January data). Jackknife estimates of the autocorrelation coefficients and their standard errors from such a sample are obtained by omitting each year once and recomputing the autocorrelation estimates. Monte Carlo results for several distributions show that the critical values of the test statistics can be based on the Student's t distribution. Regional analogs of these test statistics are derived from the jackknife estimate of the mean lag 1 autocorrelation coefficient for the sites of interest. In a similar way one can get a single test statistic for a season or the whole year. As an illustration it is shown that the lag 1 autocorrelation coefficients of the simulated daily temperatures of the Canadian Climate Centre second-generation general circulation model are significantly below those of the observed temperatures at De Bilt for most seasons. Over western Europe there is no statistical evidence of differences in autocorrelation between the 1 ? CO2 and 2 ? CO2 runs of this model.