We start from a profound epistemological question raised by Milanković, that is to say the stark contrast between the regularity of astronomical cycles and the irregularity of the atmospheric response, and we point out this correspond to a fundamental problem of renormalisation when upscaling the system up to climatological scales. We first clarify that two distinct representations of spectral analysis yield two complementary insights, while they appear at first glance opposite. Indeed, we show that both agree on the prevalence of the nonlinearity of the climate response. We generalise this spectral analysis with the help of a multifractal analysis of the Vostok data. This provides evidence of a strong intermittency, in fact nonlinearity in nonlinearity. Therefore, the spectral scaling is clearly generated by nonlinear processes, and out of reach of linear stochastic differential operators.