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)
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I would love to see CAGW convincingly refuted, but this paper does not inspire confidence. The URL has Nature_Paper in it, but I can guarantee you Nature did not approve this for publication. Possibly it was submitted to Nature, which means exactly nothing. Also, I hate the fact the authors use the term “robust.”
Someone ought to be able to figure out how to do the type of testing they are suggesting here, but I am not convinced they have it right.
Another paper which seems to use some similar tests claim “significant (dangerous) anthropogenic interference with the climate system has already occurred.” See http://www.springerlink.com/content/h0tx44h508602755/
“JDN (20:43:35) :
[…]
summarize their independent variables, justify their choices of variables (e.x. they introduce rfCO2 without explanation”
“In Table 1 we provide details of the classification procedure for the radiative
forcing of CO2 (rfCO2).”
Questions?
Putting a paper such as this on WUWT adds fuel to the fire from RealClimate, Tamino et al. There doesn’t seem to be an identifiable Journal title, volume part or page number on the pdf and I can’t find anything except Nature-09 on the net. I doubt very much if this paper is destined for Nature, not because it is anti-AGW but because it isn’t that flash. Possibly it is a trawl by Nature to provide info on upcoming papers but that’s just a guess. I don’t think you do your cause any good at all with stuff like this, it provides too much ammunition for those who seek to discredit your blog.
Don’t want to sound like a broken record but I probably do.
It would be wonderful to see an analysis of actual climate model outputs against reality.
Rather than a fictional result (CO2 correlated to temperature) which everyone including the IPCC all agree won’t produce good results.
A real climate model has more than CO2 affecting climate.
Surely someone can produce an analysis.
@Alan Wilkinson
I simplified too much. The radiative forcing of carbon dioxide is logarithmic in the concentration. The authors correct for that.
Still, rfCO2 is I(2) — in this and other studies — that is, the second partial derivative is positve. Temperature is only I(1) — that is, the first partial derivative is positive but the second is not.
I(2) cannot Granger cause I(1).
R. Gates (13:53:54) :
“From both a mathematical standpoint, and the very marginal “science” involved in this paper…it is pure crap.”
Actually, if they were using a computer with available “climate data” then, I totally agree with you!
The one thing I have learnt in the last few years is that we are light years away from being able to model chaotic systems, especially when one ….fudges the figures but as usual I will leave it to Lord S. McIntyre to debunk the numbers.
Honest! The Queen will be over to Canada very soon to get the blade out on S.M. if only to shut up “He who Talks to Plants”!
Richard Tol (01:02:24) :
I’m surprised you say mean global temperatures are only I(1). A polynomial fit to GISTEMP, 1880 to date, shows a positive coefficient in the quadratic term:
http://img638.imageshack.us/img638/7125/gistemppoly.png
“Still, rfCO2 is I(2) — in this and other studies — that is, the second partial derivative is positve. Temperature is only I(1) — that is, the first partial derivative is positive but the second is not.”
It means the second derivative is stationary, not necessarily positive.
It is true that if temperature really is I(1) then it cannot be driven by CO2. But if you take an I(1) process and add a very small amplitude I(2), the result is strictly speaking I(2), but looks I(1) on short time scales. You need to collect a huge amount of data for the I(2) behaviour to come out.
I’m beginning to think that what this paper says is that the null hypothesis – of any correlation being spurious/temporary – cannot be rejected on the evidence available. That’s not the same as the positive statement of saying the correlation is entirely spurious/temporary. It’s also nothing to get excited about.
As a sea surveyor (looking at seabed rather than crawling through bilges looking for rust holes like a marine surveyor) with a degree in Marine Biology and Biochemistry my statistics is not what it should be and “cointegration” is way over my head, but it does make sense in a general sort of way. I’m reminded of Le Chatelier’s Principle in chemistry, wherein a system in equilibrium will act to a perturbing influence in such a way as to restore equilibrium. A couple of years ago New Scientist (when I was still subscribing) published a puff-piece for AGW replete with graphics that showed that the anthropogenic flux of CO2 was about 7% of the annual natural flux. Now I know of no demonstrably stable system which is so sensitive to such a small perturbation.
It strikes me that the GCMs all start from the assumption that CO2 is a major contributor to atmospheric temperatures by means of a known ability to absorb and re-emit IR radiation. That part of the science is certainly settled, but what isn’t is the overall effect of such in the vast, turbulent and probably chaotic atmosphere in general.
Were one to start from the data (and as both Pa Annoyed (16:46:44) and Sherlock Holmes pointed out, “it is a capital error to theorise without data” (although perfectly permissible and indeed essential to hypothesise), one might note that as the world gets warmer CO2 levels are seen to increase and vice versa, with a 400-1,000 year lag in each case. This indicates that CO2 is most unlikely to be the cause of temperature rise. Instead, since CO2 is emitted by soil organisms, the oceans, peat bogs and permafrost as temperatures rise the a priori assumption must be that the balance point of the system shifts towards higher CO2 levels with higher temperatures and any sudden injection of CO2 will cause a temporary spike in the atmospheric CO2 levels before a near equilibrium is restored. This paper, so far as I can understand it, seems consistent with this idea. Comments please.
Ian (00:32:39)
Oh my god, you mean it’s not peer-reviewed??? Burn it immediately.
Ian, you (and Tamino and the like) miss the point entirely. The reason we put papers like this up here is not to claim that they are right. It is to find out if they are right.
Unlike you, we don’t give a shit where it was published. Instead, we care if it is true. Only by submitting a paper to the full glare of public examination can we determine if it is worth keeping.
But we certainly don’t decide that on whether it is a nature trawl, or whether it is published or peer reviewed. Instead, we call on the extended community to comment and find fault with the substantive aspects of the paper.
Now, a complex paper like this, only some people can comment on it. But I understand what they are saying. I don’t have an opinion yet on the validity of the paper, but I find the approach fascinating. A number of people have already either raised objections, or validated, sections of the paper and the ideas therein.
That’s the process of public science. Yes, I know it is not pretty … but it is damned effective, much more so than the pathetic process that passes for peer review in these parlous times …
Willis Eschenbach (04:08:40) :
That’s the process of public science. Yes, I know it is not pretty … but it is damned effective, much more so than the pathetic process that passes for peer review in these parlous times …
Seeing that a paper was published in certain reputable journals would probably shuffle it higher up my intray if the subject matter was relevant to my interests.
Nature isn’t one of them.
If I thought it was important I’d then bring it here for an airing. WUWT provides a much more thorough and transparent process.
Pa Annoyed (03:30:38) :
The paper states:
“We confirm previous findings (ii,iii,v,vi,iix) that the radiative forcings of greenhouse gases (C02, CH4 and N2O) are stationary in second differences (i.e. I(2)) while global temperature and solar irradiance are stationary in first differences (i.e. I(1)).”
There is no analysis given in this paper that temperatures are I(1) – it is just asserted. As for the previous findings, if you look at the latest Kaufmann work they cite, it actually says “temperature itself is not I(1)”, hardly what this paper claims to confirm.
This is a sloppy and obscurantist piece of work.
Gary Palmgren,
I am very sympathetic to your viewpoint, as I do understand the physics, and have actually carried out infrared absorption and reflection measurements on a variety of materials, liquids and gasses. I also understand non-linear dynamics of systems, and how difficult it is to make sense of complex time series data where dynamic non-linearities are involved. One discovery I made was that much of the published data for infrared absorption and its magnitude, was that many of those who carried out the experiments had failed to clear their experimental method of the differences between absorption and reflection. So called absorption and ‘extinction’ coefficients can be found to have large errors – the optical density and refractive index are subject to the density and the admixture of other gasses, in particular water vapor. I therefore consider that the Miscolczi paper contains some good sense, as does the Beenstock paper’s analysis of the data. What is worrying is that I can find no current experimental science – the measurement of gas columns in a laboratory environment, in a correctly designed experiment. The case seems to rest on Laplacian computer models, and the interpretation of remote sensor data that appears to support the model. This is not good science, and would bring howls of protest from an older generation of physicists. To find good experimental results you might as well take down R.W. Wood’s ‘Physical Optics’ of 1911 which does describe well conducted experimental results on gaseous absorption, both the near and far infrared.
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.
‘Street (20:08:02)’ put it very well when he made the comparison between economics and climatology.
Methodologically speaking, climatological modeling looks much more like economic modeling, than modeling in the exact sciences. Climatology, just like economics, relies mainly on non-experimental data to verify it’s hypotheses (i.e. models).
The main differences are:
(1) economists know econometrics, and climatologists just wing it as they go along (ask E. Wegman or J.S. Armstrong).
(2) economists have access to many different time series. This is quite important if one realizes that, in (statistical) time series modeling, an observed series is treated as a single drawing from an (unknown) data generating process.
In broad lines, the paper posted above empirically tests whether we find CO2 effects on temperature. The Time Series methods employ assume very little about the underlying data generating process; it is a statistical procedure, much akin to measuring a correlation. Very simply put: rather than looking at the relationship between levels in the variables studied, one looks at the relationship between growth rates (or changes in growth rates), which should be just as solid if the hypothesized relationship between levels is valid.
The conditions tested are furthermore necessary for causality, rather than sufficient. This paper therefore rejects the necessary conditions for measurable causality. I say ‘measurable’ because it is quite plausible that CO2 levels impact temperature in some way. It is however very unlikely that they impact them such a straightforward and unambiguous manner as proposed by Mann et al.
Furthermore, methodologically speaking, what amounts to ‘scientific proof’ of a hypothesis in climatology is very disturbing. The argument propagated by both Mann (in his recent Washington Post editorial) and Jones (in his recent BBC interview), is that Man-Made CO2 is the culprit because the coefficient is significant in their regression.
Note that this is also their ONLY empirical/fact-based argument, the rest of their ‘arguments’ are hypotheses (i.e. models) and anecdotes.
Mann wrote: “Scientific evidence for the reality of human-caused climate change includes independently replicated data documenting the extent of warming; unprecedented melting of glaciers; rises in global sea levels; increasingly widespread continental drought; and models that predict all of these things but only when human impacts are included.”
Rough translation:
(1) We tried to explain the variance in temperatures with a model including total CO2, the coefficient was insignificant.
(2) We then split total CO2 into Natural and Man-Made CO2, where the latter series (which represents only a small part of total CO2) is equal to 0 for most of the last millennium, and shows a positive trend since the industrial revolution.
(3) In our new regression, the positive Man-Made CO2 trend (now entered separately from Natural CO2) coincides with the modern warming trend, and therefore ‘sucks up’ the variance. The Man-Made CO2 variable then ‘explains’ the Modern Warming.
I furthermore bet that the coefficient on the Man-Made CO2 variable is very high. This shouldn’t surprise anybody. You are dividing a warming trend with a (relatively) small Man-Made CO2 trend, the outcome will be a very high amount of ‘warming’ per unit of Man-Made CO2.
Do note that it is only of marginal importance how exactly Man-Made CO2 enters the right hand side of the equation. As long as the hypothesized relationship is positive, it is very likely to be ‘validated’ by regressing two positive trends on each other.
From this it should also be clear why Michael Mann really wants to eliminate the Medieval Warm Period from the official temperature record. If the temperature record is flat (i.e. has low variance) before the Modern Warming Period, his Man-Made CO2 variable will have an even stronger and more statistically significant effect (the temperature variance in the past won’t ‘disturb’ his two-trend regression).
..
This type of analysis wouldn’t pass as a Bachelor thesis in econometrics at the university where I graduated.
Tom P,
The paper says “Consistent with our argument that temperature itself is not I(1),…” which isn’t quite the same. They’re trying to argue that heat does not accumulate, but is determined directly by the external forcings at the time, some of which do accumulate, and therefore temperature is due to those forcings.
However, I can’t see where in the paper they examine whether temperature is I(1). The nearest I’ve found is a comment to the effect that if there was a stochastic trend in temperature, it would be unstable, and would not keep returning to an equilibrium level. But that statement depends on the timescale you examine it over. In the 50-100 year short-term it will look very much like a stochastic trend.
There’s a lot of “consistent with” going on, which looks like affirming the consequent.
But you’re right. Both papers fall short of showing all their working.
@Tom P / Pa Annoyed
I was just trying to summarise the paper for people who do not know econometrics.
The paper does not volunteer many details, but Beenstock is a fine econometrician. Besides, the core argument — the different orders of integration — is well-established.
The innovation of the paper is the polynomial integration.
Hmm. I’m a sceptic but I don’t need this kind of stuff to augment my arsenal. This has to much of a “presto” feel to it. I think that what there is of climate science has been spread too thinly. If we don’t really know half of what drives climate, a hermetically sealed mathematical proof of anything by the buy-low-sell-high science isn’t going to make climate science settled anymore than the political scientists were able to. With AGW on the run, we are going to get a bandwagon effect and carloads of crap like we got when AGW was the plat du jour (farmers noting that their sheep were getting smaller so they would cool better, etc).
Joe (18:22:04) : JonesII (16:22:37) : It´s the SUN….! PERIOD.
“If it was truly the sun then it would only effect heat and cold. Not evaporation or precipiation that is increasing.”
Where does your information on increasing evaporation/precipitation? The atmosphere is drying out: http://i38.tinypic.com/30bedtg.jpg
Richard Tol (06:24:26) :
Do you know of any evidence that establishes temperature as I(1)?
Beenstock may be a fine econometrician, but he appears to be directly contradicting Kaufmann who does seem to have done the seminal work in this field. I don’t see how they can both be right.
Leif Svalgaard (20:35:49) :
red432 (18:52:40) :
Sounds like mumbo jumbo to me.
To me too !
Of course the arrival of mumbo jumbo conjurors in the skeptical camp is pretty good evidence that the tides of intellectual fashion are turning, perhaps decisively. These guys may not know how to predict climate, but they know how to get papers published…
A car drives down a road. Carefull measurements are taken to determine the altitude of the top of the car and the top of the road. From time to time the car hits a bump in the road. This cause a slight increase in altitude of top of car followed by diminishing oscillations due to the suspension system. someone hits the breaks. The front end of the car dips, the rear rises, oscillations damp out to zero. An extra person gets into the car. Slightly lower altitude until they get out. Road goes over a hill. At bottom of hill altitude at top of car starts to rise but the change in angle causes a slight compression of the susepension that oscillates and damps out. At top of hill, the reverse, as slight decompression happens. At bottom of hill, slight compression.
Now take reams and reams and reams of such data. Fix the altitude of the road and the altitude of the top of the car as stationary 1st order. All other inputs as 2nd order. Conclusions one would draw about things that affect the altitude of the top of the car:
1. Bump in the road causes an oscillation in altitude, but no long term change.
2. A person getting in the car makes a long term change, but it goes away when the person is removed.
3. Changes in incline of the road (bottom, crest and top of hill) cause both temporary oscillations in the altitude of the car, as well as long term changes in the altitude of the car that mirror the altitude of the road.
4. When several changes occur together (change in incline, bump in the road, stunt person leaping from one vehicle to another) the combination of oscillations can be much larger, but any conclusions about long term altitude must trends must be derived by removing the stationary 1st order to reveal the balance of change due to the 2nd order.
So… what this technique arrives at is to show that a bump in the road causes an oscillation in car altitude but no long term change. If one were to measure during a period of the initial oscillation only, one would incorrectly conclude that the bump had established an upward trend that could be extrapolated until the cars wheels were no longer touching the road. Changes in altitude of the road itself (the hill) also induce temporary oscillations as well as long term altitude changes, as does the stunt person leaping onto the car.
Unfortunately for the zealot demanding smoother roads (built by him of course) the bump in the road will not launch the car into space. Gravity works. The paper simply shows that when the primary drivers which are the irradiance of the sun and the temperature of the earth are isloated as first order, 2nd order inputs such as CO2 increases appear as temporary oscillations, not long term changes. Thermodynamics works.
And I bet that the statistics used to analyse tree ring data for the Hockey Stick, falls into the same trap.
Stationary statistical methods used for non-stationary data leading to spurious correlation.
Didn’t Steve McIntyre say this some time ago?
@Tom P
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?
B&R critique previous studies at the top of page 3.
Just to follow up on this, I plotted the 1st and 2nd derivatives of monthly CO2. The 1st derivative gives you a wave that matches monthly changes to the solar ephemeris, which is the distance between the sun and earth.
The 2nd derivative gives you basically the same thing, but with a longer sequence wave repeating in the series. This longer wave generally matches the up and down trends of both cosmic rays and monthly sunspot groups, at least between the period of Sept, 1983 to Dec, 1995. Between Cosmic Rays and Sunspot groups, I’d give an edge to cosmic rays as both the cosmic rays trend and the 2nd deriv CO2 trends are flat, where as the sunspot trend edges up slightly.
So basically, I’d say if this paper has hit upon something, it’s that there’s a correlation between the 1st deriv of CO2 and the solar ephemeris, and the 2nd deriv of CO2 and reversed cosmic rays.
Anyone wanting to repeat this analysis or explore it further can get the data I used from my Climate Scientist Starter Kit here:
https://sourceforge.net/projects/cssk/files/Climate%20Scientist%20Starter%20Kit.zip/download
scienceofdoom (00:37:45) : “It would be wonderful to see an analysis of actual climate model outputs against reality.”
see http://hockeyschtick.blogspot.com/2009/12/22-climate-models-v-actual-observations.html
and http://hockeyschtick.blogspot.com/2010/01/highlights-from-john-christys-ipcc.html
Tom P (02:57:42): “A polynomial fit to GISTEMP, 1880 to date, shows a positive coefficient in the quadratic term”
the coefficient in the quadratic term of 5E-05 is so small that it’s essentially zero