The stratosphere, rarefied or not responds to variations in energy flow and is more sensitive because it is rarefied. To some that is "noise" to others that is information. If you are in the information group, then comparing energy to energy is better than temperature to temperature.
Using the Renoldsoiv2 SST data set for the tropical oceans, 20S-20N which is in C degrees, I calculated the equivalent energy using the S-B equation leaving the seasonal cycle. This gives you an idea of how much the surface energy changes with respect to lower stratosphere temperature.
Now in this one I converted the lower stratosphere temperature into an energy anomaly using 211.5 K as the 2004 to 2013 average temperature. That just produces bigger wiggles, so then I used a cascading 27 month filter to smooth things out. Pick a different filter and you will change the relative peaks, but I use 27 month because it is close to the QBO frequency. This filter shows that the Pinatubo effect started years before the eruption in 1991.5. Well there was an eruption prior to Pinatubo that may not have work its way out of the system yet. Pinatubo had to have an impact, but where is it?
As I said, I have no opinion of Greg's post, but I think blowing off the stratosphere is a bit rash.
Update: Well I guess is happy with what he has. Personally I think less anomalizing and smoothing is a good thing. Since I have done a bit of looking at the tropical startosphere in the past I thought I might as well add another relationship to solar.
The stratosphere is a bit unique in how it responds to the surface energy and solar energy. This compares the PMOD solar downloaded from Woodfortrees with the UAH tropical lower stratosphere. Greg mentions that the relationship changes following Pinatubo in his analysis. Well it does, it goes from being more strongly related to solar to much less. Pinatubo not only happened to hit following a down slope in the annual SST it also happened to hit a down slope in solar. Cloud cover is generally credited with the shift, but we have a lot of confounding factors.
Another one is that mystical 28 C convective trigger. Pretty much every time the SST in the tropics exceed 28 C, there is a larger than normal reduction afterwards. These pops and drops, El Nino events happen most often during solar minimums. There is not a huge change is solar intensity so there is always more than enough energy to produce an El Nino, so there is likely some internal response driving the events. I have no insight into what that combination might be, but it appears to be related to orbital/tidal phenomena. Deep convection of course messes with stratospheric ozone and water vapor just to add some more fun to the puzzle.
In any case, there is a heck of a lot going on but solar/orbital is starting to look a bit better during this slow volcanic phase. If nothing else, Greg's analysis should show there are a lot of challenges in climate science.