One thing that is for certain is that these oscillations revert to the mean over the long term, and can not be used to explain a natural secular warming trend, which is what the climate sceptics seem to be running on about recently. (realclimate.org)
In terms of explaining this period of warming, the stadium wave argues: 1910 - 1940 (warming), 1940 - 1975 (cooling), 1975 - 2001 (warming), 2002 - present (cooling)-- against a background secular warming trend. (judithcurry.com)
Figure 3 (Data sources here and here) There is a secular warming trend that has persisted since the end of the Little Ice Age in the 19th century. (pearltrees.com)