Hey Alex, I wonder if you've seen
this post by Grant Foster? It seems that the paper in question here (Rajaratnam et al 2015) has some pretty serious errors in it, and may very well be a case of "right, but for the wrong reasons". It's possibly not entirely helpful to the progression of analysing climate data.
Foster's an expert in time-series analysis who published on variable stars with the AAVSO, and has more recently published a fair bit about time-series analysis of global climate data (notably Foster & Rahmstorf 2011 as well as a good book about the relevant stats).
A classic post from 2009 called "Riddle me this" explored simply what happened if you plotted the trend from 1979 to the 1998 outlier, the steepest significant trend in the data ... then extrapolated this trend line through the more recent data to the [then present] 2009. No "pause" at all, and the same result occurs with data to the present day! More recent relevant posts may be
Slowdown Skeptic, or
Is earth's temperature about to soar?