|Figure 1. Graph of temperature trends over each 15-year period. Each point represents the trend over the preceding 15-year period.|
Now as to the last time the Earth showed a statistically significant 15-year cooling trend, well, that's a bit tougher to answer. The code I'm using cannot account for autocorrelation, which means that it is biased toward showing significant time series trends when in reality the trends are not significant. The original code also didn't compensate for multiple comparisons. Even using that extremely lenient standard of significance, however, the last time the Earth experienced a statistically significant cooling trend was from August 1957 to July 1972 (trend: -0.00424ºC per year, p-value = 0.0425). So at the very least, it's been 41 years since the Earth last had a 15-year cooling trend of any sort—and 41.5 years since the Earth had a statistically significant 15-year cooling trend.
I realized that I made a mistake in not compensating for multiple comparisons. Since I was computing every possible 15-year trend, 5% of the trends would be statistically significant by chance alone. With 1,416 computed trends, that means around 71 of them would be statistically significant by chance. To compensate for multiple comparisons, I used the p.adjust function in R to use the Benjamini & Yekutieli (2001) method for compensating for fake positives. When I did that, the last statistically significant cooling trend was pushed back in time to the 15 years between February 1943 and January 1958 (trend: -0.06929ºC per decade, p = 0.04). Again, this is without autocorrelation, so it's very likely that even that cooling was not actually statistically significant. But it's been at least 56 years since the last statistically significant 15-year cooling trend. And my guess is that if I could incorporate autocorrelation in to my code, it would be far longer than that. The current warming really started in 1910, so the safe bet would be 1910 or before.
If any of my readers know how to incorporate ARMA into a rolling regression in R, please leave a comment with the code and I'll update my analysis.
Updated R code used for this analysis
GISS=ts(Climate.1880$GISS, start=c(1880,1), frequency=12)
c(Est=co[,1], SE=co[,2], t=co[,3], p=co[,4])
rr=rollapply(GISS, width=180, FUN=func, by.column=FALSE, align="right")
rr$p.time.adj=p.adjust(rr$p.time, method="BY", n=length(rr$p.time))
plot(rr[,2], type="l", xlab="Years", ylab="15-year trend (ºC/year)", main="15-year trends in GISS surface temperature data")
text(1950, 0.03, "Warming Trend", col="Red", lwd=2)
text(1950, -0.02, "Cooling Trend", col="Blue", lwd=2)