In this study, two parsimonious statistical representations of climate variability on interannual to multidecadal timescales are compared: the short-memory first order autoregressive representation (AR1) and the long-memory “power law” representation. Parameters for each statistical representation are fitted to observed surface air temperature at each spatial point. The parameter estimates from observations are found in general to be captured credibly in the Coupled Model Intercomparison Project 3 (CMIP3) simulations. The power law representation provides an upper bound and the AR1 representation provides a lower bound on persistence as measured by the lag-one autocorrelation. Both representations fit the data equally well according to goodness-of-fit-tests. Comparing simulations with and without external radiative forcings shows that anthropogenic forcing has little effect on the measures of persistence considered (for detrended data). Given that local interannual to multi decadal climate variability appears to be more persistent than an AR1 process and less persistent than a power law process, it is concluded that both representations are potentially useful for statistical applications. It is also concluded that current climate simulations can well represent interannual to multidecadal internal climate persistence in the absence of natural and anthropogenic radiative forcing, at least to within observational uncertainty.