Climate models can correctly simulate the continuum of global-average temperature variability.

Climate records exhibit scaling behavior with large exponents, resulting in larger fluctuations at longer timescales. It is unclear whether climate models are capable of simulating these fluctuations, which draws into question their ability to simulate such variability in the coming decades and centuries. Using the latest simulations and data syntheses, we find agreement for spectra derived from observations and models on timescales ranging from interannual to multimillennial. Our results confirm the existence of a scaling break between orbital and annual peaks, occurring around millennial periodicities. That both simple and comprehensive ocean-atmosphere models can reproduce these features suggests that long-range persistence is a consequence of the oceanic integration of both gradual and abrupt climate forcings. This result implies that Holocene low-frequency variability is partly a consequence of the climate system's integrated memory of orbital forcing. We conclude that climate models appear to contain the essential physics to correctly simulate the spectral continuum of global-mean temperature; however, regional discrepancies remain unresolved. A critical element of successfully simulating suborbital climate variability involves, we hypothesize, initial conditions of the deep ocean state that are consistent with observations of the recent past.