It happens that I picked my start data before I was familiar with the data, and based it on publication dates of documents, what the diagrams in the AR4 show etc. I discussed the choice of the start date before I even learned how to do the corrections for AR1 noise. That said, I’m entirely aware that some don’t believe this. But I can do nothing about that.

I’ll edit the sentence– you’ll see my next post clarifies this specific point.

a point that you seem to skip over in the text here, though you clarify slightly in comment # 3229…

– the Tamino time interval is from January 1, 2000 to the present. However, the interval you’ve been working with generally up to now has been January 1, 2001 to the present. Those are quite different starting points, and a year’s worth of data between in one and not the other.

In particular, when you say here that “Many will recall that, if we apply the method I just applied above (and a few others), the 2C/century IPCC projections for warming early this century have been, and are falsifying right now, using merged data through April.” – I believe this is untrue, if you are referring to a starting point of January 2000 rather than 2001.

Which then goes to the issue of cherry-picking…

I think warming is certain. I think it’s proven that we caused at least some of it.

What I think we don’t know is precisely how much warming there really is, and how much we caused. But there is at least some warming, and we caused at least some.

I really doubt that’s going to reverse or be disproven.

On the rest, I agree with you generally. If Tamino has the skill he says, one would expect he could test the statistical significance of a trend using something other than the rather obscure method discussed in the lightly cited Lee & Lund paper.

As far as I can tell from reading, Cochrane-Orcutt is better when there is a lot of red noise (even if the system is not perfectly AR(1)), and ARMA is better when the system has correlation but it’s not AR(1).

I don’t know ARMA yet. So, I normally apply C-O.

I also agree with you in principle that I should avoid flawed methods like the Nychka method (which is originally documented in a laboratory type report, and later discussed as a suggestion in Lee&Lund. Based on the 5 citations, the Lee and Lund paper has not exactly taken over the statistical world.)

Nevertheless, blog-rhetoric being what it is, the consequence of my ignoring the method entirely leads to accusations that I don’t use the method becaise ot gives results I don’t like. There are plenty out there who suggest I pick CO because it falsifies where this Nychka method would not.

As few people would understand the statistical arguments against the Tamino method, the fact is I need to respond to both prongs of the argument.

First: Tamino/Lee&Lund/Nychka method is NOT better than CO. Tamino’s method (Nychka) is an oddball, short cut method. Lee&Lund advise that it might be of value for those who don’t want to go to the trouble of doing the problem right. I’ve responded to that.

This argument should be enough for those who read and understand what the Lee&Lund paper actually says about the Nychka method. (And what they said is what managed to get through peer review at Biometrika.) But right or wrong, it’s not a persuasive argument to those who don’t understand the Lee&Lund paper.

Those people do understand the second prong of the argument which is that I use CO because the Tamino/Lee&Lund/Nychka method would not falsify 2C/century.

This is untrue. If we use the oddball Tamino/Lee&Lund/Nychka method, we also falsify 2C/century since 2001.

This particular blog post is a precursor to making the argument above. After it’s made, I can respond to people’s questions when they ask them. I am asked this all the time btw.

For the rest: better methods of hypothesis testing would be great! But for now, I do want to show a few things using the Tamino/Lee&Lund/Nychka because there are counter arguments out there. I could do the perfect tests, and I would still need to show people the results using that silly method.

1) The adjustment to the standard error of (OLS) regression noted in the text, “Neff=N (1-ρ- 0.68/ √N )/(1+ρ+ √N),” is the adjustment of Nychka et al, ” Confidence Intervals for trend estimation with autocorrelated observations,” equation (5). It is an attempt to put a better confidence interval around inefficient (i.e. highly dispersed) parameter estimates of the OLS estimation under first order autocorrelation. But why use the inefficient parameter estimate in the first place? If one doesn’t have software with time series estimating routines to estimate autoregressive and/or moving average components of the error term, one can still use a Cochrane-Orcutt or Hildreth-Lu algorithm implemented in a spreadsheet macro. These estimates have much better statistical properties under first order autoregression and somewhat better, albeit at times worse, properties under messier versions of serial correlation. Why Mr. Tamino, whoever he may be, chooses to use OLS with a correction appears to indicate either a real misunderstanding of time series estimation or an attempt to skew the results. There is free software — particularly R, but also some more specialized econometric packages — for the PC that will do pretty good jobs at time series estimation, and of course any academic has at his or her disposal all kinds of software.

Had Tamino done that, he would have found a very messy ARMA structure. My estimates of the structure for the HadCRUT3v series have the following coefficients, S.E.s, t-stats, and significance levels:
Variable Coefficient Std. Error t-Statistic Prob.
C 0.163232 0.143724 1.135731 0.2594
TIME 0.000926 0.000472 1.963259 0.0530
AR(1) 0.246250 0.129654 1.899291 0.0610
AR(2) 0.260135 0.109868 2.367713 0.0203
AR(3) -0.160860 0.092803 -1.733357 0.0868
MA(1) 0.219272 0.080283 2.731254 0.0077
MA(9) -0.267588 0.075713 -3.534243 0.0007
MA(10) -0.219605 0.077899 -2.819084 0.0060
MA(16) -0.654157 0.065740 -9.950684 0.0000
(with Newey-White HAC S.E.s for 2000:01 – 2007:07 in monthly anomalies)
Close to a rejection of no trend, but still not significant. Of course, throw in a decent explanatory variable, say the Multivariate ENSO Index, and you will get significance in the trend although not in the coefficient of the MEI(lagged once).

I am certain with a little work (i.e. cheating by specification search) I could have found a ARMA structure and estimating procedure, e.g. GARCH, that would give me a significant pure trend fit if I needed to report it. But I still wouldn’t use the Nychka adjustment because it is an adjustment on an estimating procedure I know, a priori, shouldn’t be used for significance testing of trends.

So my (multivariate statistics) moral is: Don’t encourage bad technique by repeating it. Just go a do it the best way you know how. Lucia, you know how to do Cochrane-Orcutt. Use it where you thing the AR1 coefficients are large. (OK, in this segment of data, the AR1 does not appear large, but REMEMBER the particular representation of the ARMA structure is NOT unique. With something as messy as the structure above, there are probably other just as good ways of representing it, presumably some with large AR1 values.)

2) Re comment 3220: Lucia, I am not certainty what the +/- 1C/century uncertainty refers to. Presumably that is the off-the-cuff estimate of the standard deviation of some estimate in the context of some probability model. Presumably, it is not the standard error of the trend slope (expressed in degrees per century) for the sample of monthly observations form 1990:01 to 2008:05? Could you elaborate on what the variable/model is?

The trend postulated by Steven Mosher of 0.2C/d isn’t too interesting with just the recent data – which you rightly say is too little.

But the longer term trend has a lot more data anyway.

The A in AGW is all about the trend accelerating since the early 1900s. That is, there’s one more layer of obfuscation. There’s the historical climate trend, the current climate trend, the current weather “noise”, and then measurement bias, and measurement error.

If the historical climate trend is .2C/d – from data measured prior to massive carbon dioxide production – , and the current weather is pushing ‘down’ such that we’re seeing “no statistically significant warming”, what does that say about AGW?

So far, I don’t see the broad hypothesis in any particular danger. Distinct warming still remains for last century and since mid-century. Moreover, their is more warming in the second half of the 20th century than the first. These are persuasive signs that support the broad hypothesis.

I don’t have a particular problem with the switch from CO2 alone to the broader GHGs. They have radiative properties also. But, the fact that other gases cause problems complicates the solution. After all, CO2 caps do nothing for Methane.

I do agree with you there are problems with the switch to “climate change”. It’s a diffuse term, and makes everything rather confusing. To test whether a theory, set of theories, a collection of models, an esteemed panel, or a group of psychics has predictive ability, we need clearly stated quantitative predictions. With regard to AGW, that means, we need to the prediction to tell us a) what is going to change, b) where the change will happen and b) how much will whatever it is change.

With regard to AGW, at least we knew that the claim was a) global temperature would change, b) this would apply to the average surface temperature over the entire planet and c) the global temperaure would go up and amount “C” in some time “t”.

In contrast when I hear the word “climate change” I have no idea what the term is supposed to suggest.

I’m going to have to do that, as it tells us something about Rahmstorf. The idea that one can even begin to say the most IPCC projections were “right” or “wrong” in any way that suggests getting the uncertainty on the slope to within 0.5C using data not collected before the projections were made is nuts. The 95% uncertainty in the slope since 1990 is about ±1C/century!

It would be interesting to see his response to Lucia’s analysis.

However it would be nice if the satellite data was used in your falsification models instead of relying GISS which pardon me is UHI influenced?

For the ‘main’ hypothesis test, I use A merge of 5 sources that include land and satellite data. I also show results for each group individually from time to time. (Data from all five always on the graphs.)

For this test, I used GISS and HadCrut, to parallel Tamino. He got in a bit of a snit that a nearly anonymous poster said there was “no statistically significant warming this century”. Interestingly, he “proved” there was using the exact method that he claims I can’t use to prove 2C/century is currently falsified. (That is, one can exclude it with a statistitcal significance of 95%.)

So, now, if you run around saying this, and someone points you to Tamino’s post, you can point them here and shown that “no statistically significant warming this century” is currently true.

I’m certain that eventually it won’t be. But I suspect if I tell you that, you’ll know that at least I’m willing to accept that sometimes weather noise actually does wander into regions where I have to either say: a) No, I can’t prove that yet or b) No. Right now, the data aren’t looking so great!