It is often stated that global temperature has increased over some specific time frame. Few realize there are different ways to answer this question, and the increase may not actually be significant, particularly in view of persistent correlation between temperature over long time scales (LTP).
In Statistical analysis of hydroclimatic time series: Uncertainty and insights Koutsoyiannis evaluates two publications using two different approaches to this issue: the evaluation of trends as done in Cohn, T. A., and H. F. Lins (2005), or as the simple change in temperature between two points as in Rybski et al. (2006).
Cohn and Lins  used as a test statistic the slope of a linear fit to the time series to test whether or not a climate variable has changed in a statistically significant sense, over the available observation period. Rybski et al.  proposed essentially the statistic D(k)(i,l) := X(k)(i) â€“ X(k)(iâ€“l) to test whether a or not a climate variable, defined on a time scale k, has changed in a statistically significant sense, over a period of l years (starting from year i).
I did a similar thing to Rybski in a recent post July 2008 Global Temperatures observing that the temperature increase of the lower troposphere TLT satellite measurements since 1979 was not significant. This attracted a lot of criticism at the skeptical-leaning ClimateAudit, and I said I would post more details. However, the paper by Koutsoyiannis already shows the analysis using the Rybski framework and the CRU data series, over a range of parameter values, and finds the same thing — no justification for believing that the underlying global temperature has not been been other than static.
It may be of some interest to apply this pseudo-test to the CRU data series. The application is shown graphically in Figure 2, for a double-sided test for significance level 10â€“2 and for the SSS case, using all possible integer lags l/k from 1 (l = 30) to 4 (l = 120). In neither case the pseudo-test resulted in rejection of the null hypothesis (no change), although it comes close to rejection for 2005 for l/k = 3.
I applied the same kind of test as Rybski and Koutsoyiannis in a limited way to the satellite RSS/MSU series TLT for the last thirty years, and found that the temperature change from July 1979 to July 2008 was also not significant. The figure below tells the same story for a different temperature series (CRU) and a wider range of parameter values, that the difference between time of publication and every past temperature is not significant. As temperatures have now decreased somewhat, the difference in temperatures between all points in the record is even less significant.
Original Caption: Figure 2 Graphical depiction of the pseudo-test based on StD[D] with known H. The continuous solid curve represents the CRU time series averaged over climatic scale k =30. The series of points represent values of D for the indicated lags l/k. Horizontal lines represent the critical values of the pseudo-test, which are the estimates of StD[D] times a factor 2.58 corresponding to a double-sided test with significance level 1% and assuming normality (only the positive critical values are plotted).
While the two approaches, fitting trends and testing difference in temperatures answer the same question there are reasons to think the Rybski approach has advantages in a LTP framework. Mainly, D(k)(i,l) does not depend on a fitted model (as e.g. a linear fitting to the data). This means that all the assumptions inherent in using linear regression for measuring trends are avoided. In particular, in LTP the correlation between terms persists even at very long time scales, and this violates the linear regression assumptions. There is less uncertainty about the form of model, providing LTP is accepted, hence less uncertainty about the variance, and about the reliability of the test.
Another advantage of ditching trends as a concept is that there are a host of other useful concepts that can be applied to the generalized model. One of these is ”mean reversion” (eg. see http://www.puc-rio.br/marco.ind/revers.html). As usual, financial time series analysis is light-years ahead of climate science. I am sure there are other concepts that could be applied, such as conservative vs dissipative dynamical theory, that can be more easily given physical interpretations. But you need to give up on trend analysis.
I was going to repeat some of the bile directed at my analysis by bender and others at CA, but frankly I couldn’t be bothered. Essentially, bender thinks trend analysis is the only ‘correct’ analysis for the global warming question. Suffice to say that if my analysis is ‘trash’ then so is Rybski et al. 2006 and Koutsoyiannis 2007. It remains for me to perform the analysis using the RSS/MSU series with a monthly time step, using a greater range of parameters and the standard deviation equation (10) derived in Koutsoyiannis 2007. I don’t expect the result will be different from the original post — no reason to believe temperatures have increased since 1979.
Cohn, T. A., and H. F. Lins (2005), Natureâ€™s style: Naturally trendy, Geophys. Res. Lett.,
32(23), L23402, doi:10.1029/2005GL024476.
Koutsoyiannis, D., and A. Montanari, Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resources Research, 43 (5), W05429.1â€“9, 2007.
Rybski, D., A. Bunde, S. Havlin, and H. von Storch (2006), Long-term persistence in climate and the detection problem, Geophys. Res. Lett., 33, L06718, doi:10.1029/2005GL025591.