Thanks for drawing attention to the paper by Koutsoyiannis and Montanari (2007). To avoid misapprehension, I would like to note a few things:

1. We do not criticize in K & M the method by Cohn and Lins (2005). Even though we preferred to use an approach similar to Rybski et al (2006), our results are compatible with C & L rather than with R et al.

2. One of the reasons we preferred an approach similar to R et al is that their test statistic has several interesting properties as we outline in the K & M.

3. Our main differences with R et al, which led to different final results, are the following.

3a. We replaced an approximate equation of R et al for the variance of the test statistic with equation 10, which we claim it is accurate (proof: from the definition of the test statistic, D_i,l(k) := X_i(k) – X_i-l(k) we get Var[D_i,l(k)] = Var[X_i(k)] + Var[X_i-l(k)] – 2 Cov[X_i(k), X_i-l(k)] = 2 Var[X(k)] – 2 rho_l/k(k) Var[X(k)]).

3b. We considered the bias in the standard estimator of std (equation (8)), which we demonstrated that for highly autocorrelated processes can be very high (because the equivalent sample size n’ in (8), calculated from equation (6) or (7), may be very small as shown in Table 1). We also discussed the effect of uncertainty in the simultaneous estimation of H and std.

3c. We tried to demonstrate that, while proxies contain useful statistical information and, in particular, they advocate the presence of LTP with a very high H, they involve several uncertainties and are statistically incompatible to each other, so that it is not wise to use their statistical estimates in statistical testing. Thus, in our testing we used only statistics from the instrumental CRU series (similar to C & L).

3d. We avoided the use of the detrended fluctuation analysis (DFA) for the estimation of H, because we think it has several problems (as a result of which R et al. had estimated some H values greater than 1) and, in particular, it hides the statistical uncertainty involved in estimation.

Despite these differences, I think that Rybski et al. (2006) is a very nice paper and I share the opinion of Ian about its authors.

4. The focus of our study (K & M, 2007) was on understanding rather than on proposing an exact test and so we preferred analytical formulations rather than numerical (e.g. Monte Carlo) methods. The cost for this preference was the fact that the test we formed is a “pseudotest” rather than a formal one. Specifically, the test was based on the assumption that the true value of H or rho is known. This is not usually the case, so the rejection rate of the pseudotest is lower than it should (i.e. if the test does not reject your hypothesis, you are on the safe side).

Demetris

PS. As I have noted elsewhere, K & M (2007) has an interesting prehistory (downloadable from http://www.itia.ntua.gr/en/docinfo/781) .

Thanks for drawing attention to the paper by Koutsoyiannis and Montanari (2007). To avoid misapprehension, I would like to note a few things:

1. We do not criticize in K & M the method by Cohn and Lins (2005). Even though we preferred to use an approach similar to Rybski et al (2006), our results are compatible with C & L rather than with R et al.

2. One of the reasons we preferred an approach similar to R et al is that their test statistic has several interesting properties as we outline in the K & M.

3. Our main differences with R et al, which led to different final results, are the following.

3a. We replaced an approximate equation of R et al for the variance of the test statistic with equation 10, which we claim it is accurate (proof: from the definition of the test statistic, D_i,l(k) := X_i(k) – X_i-l(k) we get Var[D_i,l(k)] = Var[X_i(k)] + Var[X_i-l(k)] – 2 Cov[X_i(k), X_i-l(k)] = 2 Var[X(k)] – 2 rho_l/k(k) Var[X(k)]).

3b. We considered the bias in the standard estimator of std (equation (8)), which we demonstrated that for highly autocorrelated processes can be very high (because the equivalent sample size n’ in (8), calculated from equation (6) or (7), may be very small as shown in Table 1). We also discussed the effect of uncertainty in the simultaneous estimation of H and std.

3c. We tried to demonstrate that, while proxies contain useful statistical information and, in particular, they advocate the presence of LTP with a very high H, they involve several uncertainties and are statistically incompatible to each other, so that it is not wise to use their statistical estimates in statistical testing. Thus, in our testing we used only statistics from the instrumental CRU series (similar to C & L).

3d. We avoided the use of the detrended fluctuation analysis (DFA) for the estimation of H, because we think it has several problems (as a result of which R et al. had estimated some H values greater than 1) and, in particular, it hides the statistical uncertainty involved in estimation.

Despite these differences, I think that Rybski et al. (2006) is a very nice paper and I share the opinion of Ian about its authors.

4. The focus of our study (K & M, 2007) was on understanding rather than on proposing an exact test and so we preferred analytical formulations rather than numerical (e.g. Monte Carlo) methods. The cost for this preference was the fact that the test we formed is a “pseudotest” rather than a formal one. Specifically, the test was based on the assumption that the true value of H or rho is known. This is not usually the case, so the rejection rate of the pseudotest is lower than it should (i.e. if the test does not reject your hypothesis, you are on the safe side).

Demetris

PS. As I have noted elsewhere, K & M (2007) has an interesting prehistory (downloadable from http://www.itia.ntua.gr/en/docinfo/781) .

When I first looked at your analysis I also thought it was meaningless as well because you appeared to taking two data points, showing that they fell inside some significance interval and then claiming that there is no evidence of warming despite the fact that the majority of points in the early dataset were under significance interval and the majority of points in the later dataset were over the significant interval.

I now see that there is some theoretical basis for the test that you are doing but I have trouble intuitively understanding what this test really shows. OTOH, I don’t have any trouble intuitively undestanding Lucia’s trend analysis with all of her caveats.

Would you be able to come up with an example that would illustrate how this test works. For example, Lucia did a good job of explaining here method here:: http://rankexploits.com/musings/2008/ipcc-projections-do-falsify-or-are-swedes-tall/

When I first looked at your analysis I also thought it was meaningless as well because you appeared to taking two data points, showing that they fell inside some significance interval and then claiming that there is no evidence of warming despite the fact that the majority of points in the early dataset were under significance interval and the majority of points in the later dataset were over the significant interval.

I now see that there is some theoretical basis for the test that you are doing but I have trouble intuitively understanding what this test really shows. OTOH, I don’t have any trouble intuitively undestanding Lucia’s trend analysis with all of her caveats.

Would you be able to come up with an example that would illustrate how this test works. For example, Lucia did a good job of explaining here method here:: http://rankexploits.com/musings/2008/ipcc-projections-do-falsify-or-are-swedes-tall/

This is just to make the point that one of the authors of Rybski et al (2006) is the leading climatologist and statistician Hans von Storch. On 10 July 2008 I referred to von Storch as a leading statistician in climate science on ‘The “PR Challenge”’ thread at CA ( http://www.climateaudit.org/?p=3259 , post #10), as follows:

“In addition to their major book on statistics referred to above, Francis Zwiers and Hans von Storch co-authored the paper ‘On the Role of Statistics in Climate Research’, which was published in the International Journal of Climatology in 2004 (vol.24:665-680). One key conclusion of that paper was ‘We feel that the cooperation between the statistical and climate sciences does not function as well as that between, for example, statistical and biomedical science … [B]etter communication between statisticians and climatologists requires a better understanding by statisticians of the specifics of climate science, and a greater effort by climatologists to communicate the specifics of open problems to statisticians.”