When I do a rough fit of the Sol y Vol combination of sun spot number derived Total Solar Irradiance (TSI) and the Crowley and Unterman volcanic sulphates forcing estimate there are a lot of choices than can be made. I selected a 27 month base smoothing period because of internal lags in the tropics. There is a huge seasonal swing of near 100 Wm-2 due to Earth's eccentric orbit that has to have some reasonable settling time. 13 month is a standard smoothing choice which would show more detail than 27 months. The longer the time period selected the more information that is lost. Any time frame I select will be question by someone with an agenda or someone thinking I have an agenda. Such is life.
This is the Hadley Center SST version 3 with the 13 moth cascade smoothing. The overall fit is generally better but with issues more likely related to ocean settling times. The Vol used is still NH only which misses half the globe with more heat capacity. We are also missing 100 years of data which had more volcanic impact that would likely have some delay moving through the system.
The same data with the 27 month smooth shows less detail which may be a problem for some, but should be easier to "roughly" fit. The extra smoothing make is it simpler to determining the weakly dampen settling periods. Once that is done there can always be an attempt to fill in some of the finer points, but I think starting with too much detail too early just leads to missed opportunities.
Note that these last two charts have light blue and red bands. The blue band is the mean of the entire period and the red the mean of the 1951 to 2010 period. Both are blurred to simulate the nominal instrumental error range. No smoothing method will ever replace accuracy. What the 27 month stacked or tiered smoothing does though is create a simple band pass filter. By having a larger number of tiers you can isolate the more synchronize 27 month events.
This is a bit of an extreme example where I used 17 tiers to isolate the ~62 year AMO/Global pseudo- cyclic oscillation. If the period happens to be fairly constant you can make a prediction based on this recurrent pattern. I wouldn't count on it though since volcanic perturbations may not be so predictable :)