<p>The North Atlantic Oscillation (NAO) is a dominant mode of variability in the Northern Hemisphere with strong impacts on temperature, precipitation, and storminess. The predictive skill of the NAO on annual to decadal scales is therefore an important topic, which is often studied using (initialized) climate models. The temporal structure of a time series is closely related to its predictability, and on inter-annual time scales the observed NAO is frequently described to have power at 2–10 years and sometimes with a distinct peak around 8 years. However, the observational record is brief, and such estimates have high uncertainty. Here, we present a thorough study to address the following questions: (1) Is the winter mean NAO distinguishable from white noise? (2) Does the temporal structure of the NAO differ between observations and historical experiments with contemporary climate models (CMIP6)? To this end, we use a range of statistical tools in both the temporal and spectral domains: Power-spectra, wavelet-spectra, autoregressive models, and various well-known time series test statistics. Overall, for both the observed and modelled NAO we find little evidence to reject the null-hypothesis of white noise. For observations, the peak in the power spectrum near 8 years is, taken alone, significant in the period after 1950 but not before. However, considering the complete spectrum, significant peaks will often occur at some frequencies, even for white noise. The large CMIP6 multi-model ensemble is statistically very similar to an ensemble of similar size of white noise. These results suggest limited decadal predictability of the NAO.</p>