Polynomial Cointegration Tests of the Anthropogenic Theory of Global Warming
Michael Beenstock and Yaniv Reingewertz – Department of Economics, The Hebrew University, Mount Scopus, Israel.
Abstract:
We use statistical methods designed for nonstationary time series to test the anthropogenic theory of global warming (AGW). This theory predicts that an increase in atmospheric greenhouse gas concentrations increases global temperature permanently. Specifically, the methodology of polynomial cointegration is used to test AGW when global temperature and solar irradiance are stationary in 1st differences, whereas greenhouse gas forcings (CO2, CH4 and N2O) are stationary in 2nd differences.
We show that although greenhouse gas forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcings, global temperature and solar irradiance are not polynomially cointegrated, and AGW is refuted. Although we reject AGW, we find that greenhouse gas forcings have a temporary effect on global temperature. Because the greenhouse effect is temporary rather than permanent, predictions of significant global warming in the 21st century by IPCC are not supported by the data.
Paper here (PDF)
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Hi all. Matt Briggs here.
I’ve not had time to read all the comments, but I have, on the request of an email, read the paper.
I do not find it especially interesting and cannot support its conclusion “that greenhouse gas forcings do not polynomially cointegrate with global temperature and solar irradiance.”
What the authors did was fit a particular kind of times series model to a couple of sets of data (not the only sets). They came to the conclusion that, since their model more or less fit their sets of data, the “previous claims that carbon emissions permanently increase global temperature are false.”
There are many kinds of time series models; some will fit better than others. Regardless of how close any of them fit any set of data, no measures of fit of those models can disprove—or prove—the AGW theory.
Statistical models can add weight to the evidence that the AGW theory is true or false, but none can ever prove it false, as the authors have claimed.
Too, their model is not especially convincing and rather divorced from the physics. Also, the more a statistical model strays from the physics, the less weight we should give it.
Last, like nearly all similar analyses, the authors do not account for the uncertainty in the sets of data. These numbers aren’t measured perfectly, and that uncertainty should be carried through and expressed in the final results.
David M. Hoffer,
The paper simply shows that when the primary drivers which are the irradiance of the sun and the temperature of the earth are isolated as first order, 2nd order inputs such as CO2 increases appear as temporary oscillations, not long term changes.
Thank you for this clear and concise summary. There is nothing in this article that would prompt a person familiar with the basics of calculus to call it “mumbo jumbo.”
I am not a mathematician but I’ve read this paper with interest, and everything seemed to me quite clear and reasonable. It would be more understandable. perhaps, if the authors would use more traditional English terms such as “1st and 2nd derivatives,” instead of “1st and 2nd differences” — but again, English is not their native language.
davidmhoffer,
But the car ride is politicized and there’s a guy citing tipping point theory saying, “There’s a bomb on the bus. If the bus goes below 50 the bomb will explode. What do you do, hotshot?!”
I agree with your analogy, though.
If there’s no discernable statistically valid correlation between CO2 and temperature, then continued claims that CO2 increases will cause temperatures to rise is falsified. AGW people may wave their hands, citing physical theory and complexity as reasons why no such correlation can be found (which is like mumbling “God works in mysterious ways!”) , but for their warnings that CO2 will devastate the planet through increasing temperatures there MUST be a detectible correlation between CO2 and temperature. This paper used accpeted and sophisticated statistical techniques and failed to find such a correlation.
[quote mattstat (08:48:17) :]
Too, their model is not especially convincing and rather divorced from the physics. Also, the more a statistical model strays from the physics, the less weight we should give it.
[/quote]
A post I made just above yours which was probably approved by the Mod at the same time yours was does show a correlation between the 1st and 2nd derivatives of CO2 and the solar ephemeris and cosmic rays, respectively.
I’m not saying this proves their paper has a meaningful relationship to physics, but it does suggest that further exploration in that direct may be useful.
mattstat,
I disagree that the more a statistical model strays from the physics, the less weight we should give it.
The whole debate about global warming boils down to this simple model.
CO2 increase -> black box -> equillibrium surface temperature increase.
With sufficient experimentss you could reduce it to a simple graph of CO2 level versus long term global average surface temperature. The lack of that one simple graph is why governments are spending billions – with the end result of one day producing that graph.
One way to unequivacally produce it would be to vary atmospheric CO2 levels over thousands of years with a sweeping frequency modulation, then use a Fourier transform to find the same sweeping frequency component in the temperature records. But that would take thousands of years.
The current data set is so limited that rough curve fits are too easily produced by dreaming up a couple of confounding effects whose magnitude is essentially a guess, allowing everyone to use their favorite fudge factors to get a better looking fit and reducing the science to arguments about whose fudge factor model is best.
mattstat:
Too, their model is not especially convincing and rather divorced from the physics.>
Excellent point. Could you perhaps elaborate as to HOW it is divorced from the physics? Or do you consider confirming the laws of thermodynamics to be a divorce?
Willis,
It is fine to post a paper here to determine if it is true, but the paper was not really introduced that way. It was introduced more like “Game over. We have the paper that disproves AGW.” Indeed, that is the claim the authors make.
It would have been better if the paper had been introduced as “Here’s an interesting paper that draws very strong conclusions. It has not been published yet or accepted for publication, but let’s look at the data, methods and conclusions and see if the paper has value.”
In pursuit of that goal, I have provided a link to a paper which claims to use some of the same tests. Only this paper claims the tests prove AGW. It would be interesting to see an analysis of why the same tests get such different results. See http://www.springerlink.com/content/h0tx44h508602755/
Alexander Feht,
I assume that economists use the word “differences” instead of “derivatives” because economic data comes in daily, monthly, and quarterly clumps and so to a mathematician it isn’t really smooth and differentiable.
George Turner;
If there’s no discernable statistically valid correlation between CO2 and temperature, then continued claims that CO2 increases will cause temperatures to rise is falsified>
Not quite. What the said is that there IS a stasticaly valid correlation between CO2 INCREASE and temperature. What they show is that the amount of increase is like a bump in the road…. so the increase causes an oscillation, but no long term change. Hence their comments about the rate of increase being important like the size of bump in the road. But it is the RATE OF INCREASE the defines the size of the bump in the road, and hence the oscillations in temperature, which will damp out to zero. Not the amount of CO2 itself.
Which fits exactly with the physics.
Richard Tol (08:07:07) :
“Beenstock and Reingewertz write “We confirm previous findings” (about the order of integration) and refer to Kaufmann and co. Why do you think there is disagreement on this point?”
See my comment at (05:10:31). Kaufmann argues in work cited that temperature is not I(1), and neither would a simple polynomial fit suggest this order of integration.
Mark Sawusch (08:33:37) :
“the coefficient in the quadratic term of 5E-05 is so small that it’s essentially zero”
Not at all. It’s just that the fit is to year-squared values that are very high (e.g. 1900^2). Hence the coefficient will necessarily be small, but that doesn’t make it essentially zero.
Merv Hobden (05:19:43) :
My own opinion is that water vapor is such a powerful blocker of long wave IR – mainly by reflection, because of reststrahlen and the difference of refractive index, that CO2 effects are orders of magnitude lower. A simple water cell, with 1/2″ of water in it will completely block the longwave IR from a 300W tungsten lamp. And, the water does not boil, as the mechanism is reflective, not absortive. Below the cut off wavelength of 4.5microns, the water is completely transparent – the visible and near IR pass straight through. You can put your hand in front of the cell – there is some heating from near IR absorption, but little serious effect. Without the cell -Ouch!
Professor Richard Wood was one of the last great experimental physicists – he was the American Faraday. And I think that a major problem now is that experimental physics is almost a dead art – except in areas such as biological sciences. Most postgrads in physics reach for a textbook and start computer modelling – they would not dream of entertaining a physical experiment. The great English Physicist, Lord Raleigh, told his students that if you could not demonstrate the laws of physics with simple experimental apparatus, you did not understand them! A lession we will have to re-learn.
Apparently advice you should take to heart! The experiment you describe has absolutely no relevance to the GH effect, absorption and reflection of solar radiation by liquid water, maybe. The brightness temperature of your tungsten lamp is probably ~3000K so there is negligible emission beyond 5μm, a source ~300K would be more relevant for GH effect, of course your cell probably is glass so it would block longer IR anyway.
@Tom P
I took the series magicjava posted (global mean temperature, 1900/01-2009/03) and averaged the non-normalized data for each year (I was too lazy to make monthly/seasonal adjustments).
Augmented Dickey Fuller test (no intercept, 3 lags, selection based on SIC) on annual global mean temperature. Note that the H0 of the ADF test is that the series in fact has a unit root.
ADF test stat: -1.134301
(1% critical value, -2.587172)
One sided, MacKinnon (1996), p-value < 0.2323
Augmented Dickey Fuller test (no intercept, 2 lags, selection based on SIC)) on the first difference of annual global mean temperature:
ADF test stat: -9.720368
(1% critical value, still, -2.587172)
One sided p-value < 0.0000
At first sight, temperature seems to be I(1), as the authors claim.
It appears that the rate of increase of CO2 causes the temperature rise (see also http://www.2bc3.com/warming.html) What is the feedback mechanism that makes the increase temporary?
I would like to point out that there is a difference between econometrics, and economics. Econometrics is concerned with numerical analysis and hypotheses, which may or may not be valid.
WRT the findings on the data they examined, I find it interesting that no correlation has been found, despite the best efforts of the warmists to make the case for warming so convincing by modifying the data. Should the methodology they used withstand critical scrutiny, it would seem to be a powerful way of detecting bad data.
Thank you matt briggs!
A note to regulars. Just because you like the result of a paper don’t lose your skepticism. A statistical argument without a physical theory is nothing more than numerology.
The other thing is this. Theories, especially long accepted theories, are not in practice falsified by one observation or paper. People may wish it to be so, but in point of fact they are not. It takes a lot more work than that to remove a theory from the throne.
science of doom. you can go get the results yourself. they are available.
terabytes. Hop over to Lucia’s she works that problem and some of her regulars as well ( chad )
grumpy old man
It appears that the rate of increase of CO2 causes the temperature rise (see also http://www.2bc3.com/warming.html) What is the feedback mechanism that makes the increase temporary?>
Think of two planes suspended in space. We’ll call one of them Sun, which is radiating heat to the other Earth. At first Earth heats up. As it does so, it starts radiating heat back. It reaches an equilibrium temperature at which the amount of energy it radiates out exactly equals the amount of energy being radiated in by the Sun.
Now think of a nearly impossibly thin slice of the earth plane being converted to CO2. The amount of energy from the Sun to Earth hasn’t changed. But the CO2 resists the emission of energy from the Earth, so temperatures start to rise since the amount of energy in the system per unit mass is increasing. But this sets off a chain of other events. The amount of energy radiated by the earth plane rises a lot faster than its temperature (it goes up with the temp in degrees K to power of 4). That thin slice of CO2 is part of the earth plane, so it heats up too,and it radiates in all directions, some back to earth and some away from earth.
When the system stops oscillating, the amount of energy going from Sun to Earth will equal exactly the amount of energy being radiated back by the Earth. Hence, the change in the amount of CO2 “slice” causes a temporary oscillation, but no long term temperature change.
davidmhoffer (18:21:08) :
I love that little logic knot as well. my favorite version is this.
Skeptic1: the temperature data is all messed up.
Warmist: is not.
Skeptic1: is too.
Skeptic2: Here I show how sunspots correlate with the temperature data.
Warmist: Your pal said the data was screwed up.
Skeptic2: err, ya but.
There are of course ways to wriggle out of this knot, but the fundamental question of the accuracy of the record remain and all analysis that uses that data is subject to caveats. GIGO for one GIGO for all.
to use yet another analogy, suppose you have a river flowing at a constant rate. Build across it a damn that you can raise and lower. When you raise the damn, the lake fills up. downstream from the damn, the flow decreases…. for a while. Once the lake fills up and gets to the top of the damn, the flow rate downstream goes to the same amount it was before. Now lower the damn. As the lake empties, the amount of water flowing downstream goes up… for a while. Once the lake level gets back down to the damn level, the rate of flow downstream goes back to the same level as before.
So… raising and lowering the damn causes temporary fluctuations in the flow of water below the damn. But the height of the damn makes no difference at all. You could raise and lower the damn all you want, over the long term, the flow would average exactly the same. So, height of damn means nothing to average flow rate. Changing the height of the damn causes a temporary change in flow rate which depends on how fast or slow the height of the damn is changed.
WRT the physicality of the argument. I want to show you a little logic trick you may find useful. (Hat tip to GE Moore)
Suppose that you read a long detailed statistics paper that claimed the earth was flat. What would you conclude? and why?
assume you don’t know statistics? assume you know statistics but can find any error in the paper. Can you rationally reject this paper and it’s conclusions even IF you can’t find the error? why.
How can I reject this paper without even checking it?
George Turner (09:04:22) :
”
The current data set is so limited that rough curve fits are too easily produced by dreaming up a couple of confounding effects whose magnitude is essentially a guess, allowing everyone to use their favorite fudge factors to get a better looking fit and reducing the science to arguments about whose fudge factor model is best.
”
Yeah, I’d like to see statistical analysis done as double blind experiments where the statisticians don’t know which data sets are the actual data sets, and which are concocted data sets perhaps derived by summing together data sets from obviously unrelated domains. Then when the conclusions correctly identify the real data sets and argue that there is a relationship, rejecting the others, there might be something to it. But even this wouldn’t help if the “real” data sets themselves are possibly bogus, as in this case.
Hmmm; I note a lot of generic deriding comments (obfuscating language and similar ilk) and slights at the authors. These comments come across as textbook examples of the demean and distract method of avoiding science. AKA the AGW Religious Ecstasy kneejerk response.
With a little web surfing:
Contrary to slights; Michael Beenstock is not unknown nor is he a lightweight.
http://ideas.repec.org/e/pbe130.html
There is a powerpoint presentation that goes along with the paper; http://www.patrickminford.net/Business_Topics/BusinessTopicsCOctober2009.pdf
I read the paper and powerpoint presentation as direct challenge to the AGW central CO2 forcing issues. The author’s names and email addresses are available; I assume they welcome discussion, that is, IF you have identified their mathematical errors or have relevant counter arguments.
@steven mosher (10:22:30) :
“A statistical argument without a physical theory is nothing more than numerology.”
You are absolutely right, but a physical theory (or any theory for that matter), that is not supported by facts (or data/statistical argument) is nothing more than a false opinion.
What the authors of the paper are simply attempting to show, is that the data is not matching the theory.
Furthermore, you state:
“Theories, especially long accepted theories, are not in practice falsified by one observation or paper. ”
In this context, this ‘one’ observation, is the only observation we have, namely the development of our temperature record. In a statistical sense, the realization of our temperature series is considered a ‘single observation’ or a single draw from the data generating process we are trying to uncover.
….and you have to admit that you are in trouble if your only observation doesn’t match your hypothesis… 🙂
grumpy old man (09:50:44) :
What is the feedback mechanism that makes the increase temporary?
The two suspects seem to be humidity levels and cloud formation behavior.
George Turner (09:04:22) :
The current data set is so limited that rough curve fits are too easily produced by dreaming up a couple of confounding effects whose magnitude is essentially a guess, allowing everyone to use their favorite fudge factors to get a better looking fit and reducing the science to arguments about whose fudge factor model is best.
Well said – that is a very frightening proposition if GCMs have actually been produced this way
Ron Cram (09:07:37) :
this paper claims the tests prove AGW. It would be interesting to see an analysis of why the same tests get such different results. See http://www.springerlink.com/content/h0tx44h508602755/
Very interesting! Abstract from the linked paper:
Abstract To characterize observed global and hemispheric temperatures, previous studies have proposed two types of data-generating processes, namely, random walk and trend-stationary, offering contrasting views regarding how the climate system works. Here we present an analysis of the time series properties of global and hemispheric temperatures using modern econometric techniques. Results show that: The temperature series can be better described as trend-stationary processes with a one-time permanent shock which cannot be interpreted as part of the natural variability; climate change has affected the mean of the processes but not their variability; it has manifested in two stages in global and Northern Hemisphere temperatures during the last century, while a second stage is yet possible in the Southern Hemisphere; in terms of Article 2 of the Framework Convention on Climate Change it can be argued that significant (dangerous) anthropogenic interference with the climate system has already occurred.
Perhaps the difference is due to the GES paper only looking at CO2 and temperature, while the BR paper looks at CO2, irradiance and temperature. I think, in theory at least, econometrics techniques should give consistent results between a 2 variable analysis and a 3 variable analysis (assuming proper methods, same data set, same time frames, etc)… but for a sec let me eyeball and summarize the trends using NOAA’s summary data (assuming of course that the data is correct):
Temperature – long term upward trend since bottoming out around 1910, stalled from around 1945 to 1977/78 (http://www.climatewatch.noaa.gov/2009/articles/climate-change-global-temperature)
CO2 – exponential upward trend since the 1950’s (http://www.climatewatch.noaa.gov/2009/articles/climate-change-atmospheric-carbon-dioxide)
Irradiance – long term upward trend since the early 1900’s (http://www.climatewatch.noaa.gov/2009/articles/climate-change-incoming-sunlight)
Personally, I am quite at a loss to understand how the increase between 1910 and 1945 (~.5 C), and 1977/78-current (a smidge under .6 C) fit with a constant up-trend in irradiance over the entire period that accounts for 10% or less of warming, and an exponentially increasing level of CO2 from 1960-on – which is, as I understand it, the official explanation… but anyway
I would be very interested to see the timeframes for the two analyses. As strange as it is, I can imagine that both analyses could be technically correct if the timeframe for GES was 1960-on and BR was from 1910-on… which would then beg the question which one is more correct(?)