Friday, January 4, 2013

"Polynomial cointegration tests of anthropogenic impact on global warming" examined by Tamino

I've be challenged with another "final nail in the coffin" of the theory of society induced global warming.  It comes in the form of a paper titled: "Polynomial cointegration tests of anthropogenic impact on global warming"  By M. Beenstock, Y. Reingewertz, and N. Paldor
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Their abstract claims: 
"We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century.  
"Specifically, the methodology of polynomial cointegration is used to test AGW since during the observation period (1880–2007) global temperature and solar irradiance are stationary in 1st differences whereas greenhouse gases and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance.  
"Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated. This implies that recent global warming is not statistically significantly related to anthropogenic forcing. On the other hand, we find that greenhouse gas forcing might have had a temporary effect on global temperature."

When I looked it up on the internet I was once again amazed at how well the same few words have been astro-turfed throughout the blogosphere.  It's this astro-turfing of yet another 'final nail in the coffin of AGW' by contrarians masquerading as skeptics that has inspired me to post the following.

Now, I admit I don't understand: "Polynomial cointegration tests" any better than 99% of the rest of the population.

But, I can witness what is happening on this planet and I've been around long enough to be leery of fast talkers with tons of statistics and hubris claiming to have proven the scientific "establishment" and the "laws of physics" wrong. 

My lack of understanding leaves me to review what folks who are smarter than me have to say and it's been interesting for sure.

The best source in this instance has been "Tamino" an accomplished professional who's an expert in statistics and has examined this study.  His post is an interesting review that folks who understand this stuff are sure to find educational.  I myself found the discussion following Tamino's post even more interesting than the over my head statistics.  

So interesting in fact, that I've decided to copy a whole bunch of related comments for the curious.  I also found another discussion over at FaceBook with some information worth sharing.

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It begins with Tamino's post:

Still Not
Posted on March 16, 2010
"Those who can’t bear to believe that the laws of physics govern global temperature, still want to maintain that it’s a random walk. They base this on the fact that the ADF (Augmented Dickey-Fuller test) doesn’t reject the presence of a unit root, if you refuse to use the BIC (Bayesian Information Criterion) for model selection and you’re willing to ignore the Phillips-Perron unit root test.

"One of the weaknesses of the ADF test in the presence of a trend is that it assumes the trend is linear. But it isn’t. How might we overcome that problem? There’s more than one way to skin this cat. One is to use the CADF (Covariate-Augmented ADF test), and supply a covariate to represent the trend. Namely: climate forcing. That will give us a much better picture of the right trend to use since 1880, than just a straight line, and will eliminate that weakness of the ADF test. Fortunately, the “CADFtest” package for R implements the covariate-augmented ADF test." . . .
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{Many lines of stats later...}

"Using only data since 1975 makes it more difficult to reject the presence of a unit root, even when it should be rejected, because of the paucity of data. Yet we resoundingly reject the presence of a unit root, regardless of how we structure the test, whether or not we allow a lot of lags, whether we do model selection by AIC or BIC or HQC or MAIC. No unit root.
And if we use the Phillips-Perron test? No unit root.

But hold on — maybe there is a way we can make the ADF test fail to reject the unit root. But before we do that, let’s look closely at the structure of the ADF test. 
It’s a regression of the form:
\Delta y_t = a + bt + \delta y_{t-1} + \epsilon_t + \lambda_1 \Delta y_{t-1} + \lambda_2 \Delta y_{t-2} + ... + \lambda_p \Delta y_{t-p}  "
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{More lines of stats and formulas...}

"But hey, let’s not totally ignore all that data before 1975 just because the trend is nonlinear! Let’s use the CADF test and supply climate forcing as a covariate. And let’s be very clear about one thing: climate forcing will affect global temperature. Unless, of course, you’re willing to deny the laws of physics.

I’ll use the climate forcing data from NASA GISS. Their climate forcing data only extend from 1880 to 2003, so that’s all the global temperature data we can use with this forcing data. Since we’re using climate forcing to represent the trend, we can not include an additional linear trend in our ADF test, so we’ll select..."{check out these stats and formulas}
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{Many more lines of stats and formulas and considerations...}

"Unit root rejected.

The whole “unit root” idea is nothing but a “throw some complicated-looking math at the wall and see what sticks” attempt to refute global warming. Funny thing is, it doesn’t stick. 
In fact, it’s an embarrassment to those who continue to cling to it.
But hey — that’s what they do."

Tamino 03/16/03
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{And then the discussion following.  
I've selected from the more interesting comments in order to expose why we should show a great deal of skepticism when drawing conclusions from Beerstock et al's adventure in statistics.}

I thought the “random walk” idea was a lemon. But clearly, it’s a cherry instead.
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H A | March 16, 2010 at 5:54 pm |
Maybe it’s actually both: a Whiskey Sour.
After all, the idea of global warming as Bourbon Myth ...

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{A short digression over to:} 
Though the effect is real, climate scientists (at  NASA GISS, for example) have made a considerable effort to identify and minimize its effects within the surface temperature record.  
Some global warming "skeptics" have nevertheless greatly exaggerated its significance, claiming that it has been responsible for much (if not all) of the measured upward global temperature trend in recent decades, a claim that does not hold up under examination. 
Posted by Horatio Algeranon 
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Oh, sorry, I thought you used CO2 forcing alone (I meant to say forcing, not simply “CO2″), I should look at that dataset.
VS is testing to see if introducing a single structural break point is sufficient.
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I | March 16, 2010 at 9:16 pm |
Has VS found an analysis he wants to stick with, or does he keep introducing new ones?
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CO2 forcing alone wouldn’t make sense …
Cool trick, since we’re constantly told that all this data’s hidden from other researchers and the general public! :)
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Okay, so can you now tell us how to perform a Phillips-Perron test? If I’m reading you correctly you don’t seem to place much faith in ADF.

[Response: I've got no beef with the ADF test, but the PP test seems better. The ADF test is also known to have low statistical power when there's strong autocorrelation. Mainly it must be borne in mind that failure of the ADF test does NOT demonstrate the existence of a unit root -- contrary to the impression some give -- it simply fails to reject it. When there's little data and a nonlinear trend, that happens all too easily.

The PP test does the same kind of regression as the ADF test, but instead of including extra regressors to account for autocorrelation, it computes a correction factor not unlike as is done for linear regression as discussed ]
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Is it possible that there is a reasonable “excluded middle” fallacy that both of you are suffering from? For instance that (based on the data) it could be consistent with a random walk or with AGW? After all we’ve had a limited amount of time and only one parallel Earth. Still given the increase, along with physical arguments, the reasonable Bayesian belief is in AGW (and the tendency to not want to believe in it is wishful thinking)?

[Response: I don't see any evidence at all for a random walk. Zero. There's overwhelming evidence of a trend. Overwhelming. The only explanation that makes sense is what the laws of physics say must have an effect: greenhouse gases. That's my opinion.]
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Essentially VS’s entire argument is meant to exclude treating modern warming as fitting a linear model, so it can then be dismissed.

He’s essentially parroting Beenstock and Reigenwertz, but I haven’t found a comprehensive rebuttal of this, either because I’ve not looked hard enough or because the physical science community looked, laughed, and moved on without bothering much with it.
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M | March 17, 2010 at 6:30 am |
B&R isn’t even published…it’s a paper someone put on their webside (with a rather hopeful filename, containing “nature”) and which is now waved around in the deniosphere as “the final nail in the coffin of AGW”.
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Do you mean use a relatively small sample and silly parameters to show that you can “find” a unit root anywhere if you mistreat the data enough?
That’s a sensible idea, but it would be easier (and more compelling) to do the same test on entirely synthetic data (as Tamino has done before to make a point).
But Tamino has wasted more than enough time on something that is daft however you look at it. Perhaps someone should suggest to VS that he rerun all his tests on some synthetic data, and see how many false positives he can get? He’s the one pushing this silly idea – so I don’t see why he shouldn’t do the work….
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I didn’t know that tamino tested if the output from climate models acted like random walks
my thought is that climate models are getting close enough to reality that they should be used as “dummy data” before yelling how this test or that test shows global warming is a hoax.
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Then the conversation got sucked into a talking about Roy Spencer's shenanigans, but that's for another time.  However, on Facebook a character called Cole Pritchard has engaged some of the SkepticalScience guys in a discussion that's produced some interesting insights into this study. 

Skeptical Science With all due respect, you appear to be missing the critical points:

CP wrote:  "...the statistical methods it used were not only valid, but required..."

No, they are completely invalid, as the climate data does not show unit roots, does not consist of nonstationary random variables, and the polynomial cointegration methods the paper is based upon are BY DEFINITION invalid under those circumstances.

CP wrote:  "The whole point is that the cited paper tries to falsify the null hypothesis, and fails to do so. ... it finds that the probability of said falsification [of AGW] being a false positive is extremely small. Therefore, the paper states the the probability of AGW being a reality is also extremely small."

The paper is invalidly using the statistical techniques, therefore ITS CONCLUSIONS about the +/- probability of AGW and their null hypothesis ARE ALSO INVALID. This is not spurious, it is the essential point. If the techniques are invalid, any conclusions of the paper are unsupported by their work - QED.

Nothing more needs to be said in terms of refuting this paper or its conclusions. You requested feedback, that was given. While the feedback may not be in the (unstated) form you desired, it would be incorrect to take the conclusions of this paper as something needing refutation - since they do not stand in the first place based upon this paper.

One additional note regarding the validity of the methods used in this paper:

• The techniques of first and second differences used in this work mean that the analysis is not of the trends, the average behavior of the climate, but rather of the noise, short term variance, finite math first and second derivatives, the weather - yearly cycles, ENSO, perhaps a volcano or two, but not the smooth rise in GHG forcing. 

• Differencing removes the trends, the real data of interest - NOTHING in the differencing techniques examines long term trends. Which means (as Tamino pointed out) that the entire technique is invalid for climate studies from this aspect alone. 

• Differencing and polynomial cointegration are simply 'a priori' invalid for analyzing climate - yet another reason why this paper is not worth consideration.

The real question is why some refuse to accept this.
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Cole Pritchard With all due respect, you appear to be missing that your critical points are naught but red herrings, and you've strayed quite far off topic. 

As you seem to have missed the crux the paper, allow me to re-iterate. Specifically, the paper set out to reject the null hypothesis, and instead rejected AGW. The paper was testing the null hypothesis, and the methodology used WAS appropriate for testing **that** hypothesis. Instead it finds evidence that strongly supports the null hypothesis and therefore the probability level of AGW being a reality to be very small. As previously pointed out [self quote]:

"The null hypothesis does **not** assert the existence of any forcings. That refutes the alleged refutation of using cointegration tests." - So, pllease refrain from shifting your goalposts.
Do you understand that rejection of the null hypothisis is standard hypothesis testing? 

With what you are trying to state, the paper should have not been published in the first place. Your statements (although intelligent sounding) are rather quite nonsensical.
Do you think you know better than the editor?
... See More
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Skeptical Science Note: If the authors were really doing a proper statistical analysis, they would find CO2 causality, much as Lean and Rind 2008 did. And if they were doing a proper statistical analysis, the paper would be an interesting application of their techniques.

The major problems in the paper, however, invalidate it _far_ before they get to that point:

• They misapply a test for non-stationary series (with unit roots), and falsely conclude that temperature and forcing are non-stationary.
• Based on that error, they differentiate (difference) both until their erroneous test shows stationary series.
• Proper testing shows both temperature and forcing lack unit roots, are therefore stationary, and _time series regression is therefore the proper method_ rather than differencing. Even using the unit root they apply (ADF), on appropriate data (1975 on, linear trend with variation around it), the unit root is strongly rejected. 
• Therefore: Their paper is not even wrong.
• Note: this means their paper does not support or falsify either the AGW _or their null hypothesis_ - you can conclude NOTHING WHATSOEVER in that regard due to invalid techniques, and the initial error regarding unit root identification. There is no support there for your claims regarding their null hypothesis, no matter how you rephrase it.
• As is, any usage of this paper to rebut AGW and/or CO2 correlation with global temperatures should be considered pre-failed. Said attempts to do so should also be considered credibility seppuku.

Proper analysis, with time series regression, has been done by multiple investigators - ALL of them have found causal links between greenhouse gas forcing and temperature. 

- "With what you are trying to state, the paper should have not been published in the first place." -

December 13, 2012 at 1:59pm 

Cole does follow with another comment, but it's repetitious and side steps the points made by the SkepticalScience science guys.
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Well here's some more extra interesting reading for those curious about these things.
Bart Verheggen writings some funny, but educational stuff about the analysis and 
James Annan points out the paper was rejected by two other journals

A ‘rooty’ solution to my weight gain problem
I just love brownies, chocolate fudge cake and the like. As a result of eating too many of those –so my dietician told me- I have gained weight over the past years. According to my dietician, somebody’s body weight depends on the ratio of their caloric input and output (i.e. someone’s personal ‘energy balance’). I also  believed that. Until recently.
Here’s a graph of my body weight over the past 32 years:

PS: This post is not meant to ridicule the arguments made in favor of a unit root. It is meant to draw attention to the fact that the physical (or biological in this case) context of the quantity we’re investigating is very important. If someone is riding a bike downhill, I could wonder if the bike could have gotten to where it is all by itself, and conclude that I cannot possibly predict when the bike will reach the valley. But that ignores the (deterministic) effect of the guy who is riding the bike. Share your favorite analogy in the comments!
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Is the increase in global average temperature just a ‘random walk’?
On the previous thread, a discussion ensued about whether the observed increase in global average temperature is just a ‘random walk’. A rundown (*):
- Anonymous commenter “VS” claims
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The relevance of rooting for a unit root
So what if the global average temperature series contained a unit root? It would mean that ordinary least squares regression may lead to spurious results in terms of inflated trend significance. It would *not* mean that phsyics-based climate models are suddenly invalid or that AGW is suddenly falsified (just as gravity is not falsified by observing a bird in the sky).
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Polynomial cointegration tests of anthropogenic impact on global warming

Apparently global warming has been refuted, buy some economists writing in Earth System Dynamics:
Were I Judith Curry, I would probably be saying "wow" at this stage. Alternatively, it could just be some dross that has accidentally found its way into print after having been rejected at least twice at different journals.

The review comments are interesting, to say the least. Reviewer #2, in particular, seems awfully keen on a number of silly sceptic claims that have been presented in recent years.
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Fast talk can win the moment, but life is about more than winning today, long term survival and prosperity depends on treating today realistically.  We all know what can be done with statistics most can't understand.  Why trust that sort of fast talking flimflam over real Earth Observation and many decades of serious climatological study?

National Research Council Video Series Summarizes the State of Climate Science ResearchJune 29th, 2012 by Adam VoilandA  new video series from the National Research Council  summarizes what scientists have learned about global warming and climate change.  It’s difficult to pack decades of complex research into short video snippets, but the makers of these videos have done an excellent job. As you watch, keep an eye out for mentions of the key role that remote sensing has played in advancing climate science. Also, look for the numerous data visualizations produced by the Scientific Visualization Studio at Goddard Space Flight Center that made the cut.

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