A set of orbital forcing cycles inspired by the persistent publications of Scafetta  was added to the CSALT model (also see Related). This set was grouped into two parts. The first set comprises the identified luni-solar periods identified by Scafetta and others. These are pure sine waves with a phase giving the best residual fit. Interesting that they do indeed have a significant impact on the model fit, raising the correlation coefficient above 0.992 for a Pratt 12-9-7 triple running filter . The other factor is a sun barycentric velocity that Scafetta has identified. This also has an impact on improving the fit as seen in Figure 1.
Overall, these extra cyclic terms do improve the goodness of fit as shown in Figure 2, while being understood as subtle factors which influence the free energy state of the earth's climate. Whether these gravitational effects are actually great enough to influence the climate in as strong a fashion as Milankovitch cycles remains to be seen, but they are presented here in the interest of open-mindedness. (Edit: see  for a book length analysis of the effects)
What is very interesting is how well the orbital forcings help to recreate the pause in recent years. In a previous post, the C&W hybrid correction was invoked as a plausible mechanism to explain the recent diversion between the model and data temperature trend. Yet, as one can see in Figure 3 (below) that the recent extended pause coincides with a strong negative cycle excursion in the sum of the orbital cycles.
The attribution to CO2 is still just as strong as shown in Figure 4. The pause is barely observable once the fluctuation terms are removed leaving behind a signal with a very slight residual fluctuation.
Figure 5 is a view of the effects of the Vaughan Pratt 12-9-7 triple running mean filter. Note how it removes the sinc-related harmonic distortion induced by using a 12-month box-window moving average filter.
Whatever residual noise that is left is still highly-influenced by the strong temperature excursions. The alignment with the original peaks indicates that this is partly amplitude-dependent noise as might be observed with phase noise.
The CSALT model has much in common with historical climate data reanalysis, which one can gather from reading this comment.
CSALT model posts