Please discuss the new paper by Michael Beenstock and Yaniv Reingewertz here.

Way back in early 2006 I posted on an exchange with R. Kaufmann, whose cointegration modelling is referenced in the paper, entitled Peer censorship and fraud. He was complaining at RealClimate about the supression of these lines of inquiry by the general circulation modellers. The post gives a number of examples that were topical at the time. ClimateGate bears it out.

Steve McIntyre wrote a long post on the affair here.

[R]ealclimateâ€™s commitment to their stated policy that “serious rebuttals and discussions are welcomed” in the context that they devoted a post to criticize Ross and me and then refused to post serious responses. In this case, they couldnâ€™t get away with censoring Kaufmann, but itâ€™s pretty clear that they didnâ€™t want to have a “serious” discussion online.

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More information about the co-integration approach is here:http://www.patrickminford.net/Business_Topics/B…

More information about the co-integration approach is here:

http://www.patrickminford.net/Business_Topics/BusinessTopicsCOctober2009.pdf

I have to say that anyone who quotes without apparent scepticism the speculations of a journalist in 1975 is, in my mind, not looking reliable.

But my main complaint is the dogmatism. GHG are I(2)!. Temperature is I(1)! End of AGW.

These are from estimates of curvature (!) of a plot from curve fitting. No uncertainties cited.

And the jargon. One of the conclusions – a bullet point!

Johansen polycointegration: methodologicallacuna

Any idea what it means?

“End of AGW”

He doesn’t say that.

“Normally, this difference would be sufficient to reject the hypothesis that global temperature is related to the radiative forcing of greenhouse gases, since I(1) and I(2) variables are asymptotically independent.x An exception, however, arises when greenhouse gases, global temperature and solar radiation turn out to be polynomially cointegrated.x”

As to “Johansen polycointegration: methodological

lacuna” its from a presentation where it would be verbally explained, and it refers to the polynomial cointegration proposed by Johansen.

They say exactly that in the abstract of their paper:

” Therefore, greenhouse gas forcings, global temperature and solar irradiance are not polynomially cointegrated, and AGW is refuted.“

Not the same thing as “GHG are I(2)!. Temperature is I(1)! End of AGW.” IMHO.

I think it’s identical. Their statement on poly cointegrated is exactly their claim that GHG forcing is I(2), temp and solar are I(1). And “AGW is refuted” ~ “End of AGW” – what’s the difference?

I agree wholeheartedly – it all looks extremely dodgy. My company does a lot of non-linear modeling and curve fitting (typically Levenberg-Marquardt of course), especially for natural, geophysically perturbed, and artificial small catchment hydrology/hydrogeology. Gives one a deep feeling for the pitfalls.

The preponderance of economists involved in this cointegration stuff scares the pants off me for a start.

But I have learnt a lot from David’s good grip on statistics so it is useful to have this cointegration stuff put up here for close examination and discussion in a reasonably amicable manner (;-) It worked quite well for exploring the Miskolczi cul-de-sac, n’est pas (even if it did take us about 2 years)?

My reading and personal understanding suggests the real heart of the AGW matter lies with insufficient understanding of the inter-related roles of ET, CCNs, clouds, albedo (both due to clouds and various levels and surface albedo issues) and water vapor. As you know I also think we also greatly underestimate the role of photoautotrophic biota in this.

I have to say that anyone who quotes without apparent scepticism the speculations of a journalist in 1975 is, in my mind, not looking reliable.But my main complaint is the dogmatism. GHG are I(2)!. Temperature is I(1)! End of AGW.These are from estimates of curvature (!) of a plot from curve fitting. No uncertainties cited.And the jargon. One of the conclusions – a bullet point!

Johansen polycointegration: methodologicallacunaAny idea what it means?“End of AGW”He doesn't say that.”Normally, this difference would be sufficient to reject the hypothesis that global temperature is related to the radiative forcing of greenhouse gases, since I(1) and I(2) variables are asymptotically independent.x An exception, however, arises when greenhouse gases, global temperature and solar radiation turn out to be polynomially cointegrated.x”As to “Johansen polycointegration: methodologicallacuna” its from a presentation where it would be verbally explained, and it refers to the polynomial cointegration proposed by Johansen.

I agree wholeheartedly – it all looks extremely dodgy. My company does a lot of non-linear modeling and curve fitting (typically Levenberg-Marquardt of course), especially for natural, geophysically perturbed, and artificial small catchment hydrology/hydrogeology. Gives one a deep feeling for the pitfalls. The preponderance of economists involved in this cointegration stuff scares the pants off me for a start.But I have learnt a lot from David's good grip on statistics so it is useful to have this cointegration stuff put up here for close examination and discussion in a reasonably amicable manner (;-) It worked quite well for exploring the Miskolczi cul-de-sac, n'est pas (even if it did take us about 2 years)?My reading and personal understanding suggests the real heart of the AGW matter lies with insufficient understanding of the inter-related roles of ET, CCNs, clouds, albedo (both due to clouds and various levels and surface albedo issues) and water vapor. As you know I also think we also greatly underestimate the role of photoautotrophic biota in this.

They say exactly that in the abstract of their paper:

” Therefore, greenhouse gas forcings, global temperature and solar irradiance are not polynomially cointegrated, and AGW is refuted. “Not the same thing as “GHG are I(2)!. Temperature is I(1)! End of AGW.” IMHO.

Itâ€™s an interesting way to test challenge AGW vs the null hypothesis. The difference method makes sense from first principles. It's another way of saying that the curves are fundamentally different – and then testing to affirm that. For statisticians, how robust are these tests? i.e., 1) What are the uncertainties in determining I(1) vs I(2) for insolation vs CO2 etc.?The analysis of the temperature polynomial cointegration may have a problem in not having separated out the global temperature vs the Urban Heat Island (UHI) effect. e.g., in equation (2). Could this affect the statistics? See Atmospheric Circulations do not Explain the Temperature-Industrialization Correlation Ross McKitrick (in press, 2010). Beenstock and Reingewertz claim: â€œgreenhouse gas forcings have a temporary effect on global temperature.â€ While they show temperature and greenhouse to have a different order, I don't follow their inference that the CO2 effect is temporary. Though the incremental CO2 absorption is decreasing with increasing CO2 concentration does not mean the increase in CO2 absorption is temporary. If the enormous ocean buffer was included, then I could see the CO2 described as â€œtemporaryâ€. However, they did not mention the ocean.

I guess it says thast the system has been fundamentallymischaracterized. What is called 'model risk'.I wonder the degree to which non-linearity can affect the signfiicancetests. Eg do such relationships as T=a+b*log(CO2) get excluded? Andwhat is the role of problems with the temperature record?

The reliability of this approach can be checked simply by applying it to model data on global temperature trends with and without anthropogenic forcings. These are cited in the report of Working Group 1 of the IPCC and are easily available. Clearly, if this method does not find the effect of CO2 forcing in model outputs that explicitly include it, the method has a problem, not atmospheric science

Yes it would be worth doing this sort of reverse engineering, as it isdoing system identification, it could be checked with a range ofsynthetic known systems.

It’s an interesting way to test challenge AGW vs the null hypothesis. The difference method makes sense from first principles. It’s another way of saying that the curves are fundamentally different – and then testing to affirm that.

For statisticians, how robust are these tests? i.e.,

1) What are the uncertainties in determining I(1) vs I(2) for insolation vs CO2 etc.?

The analysis of the temperature polynomial cointegration may have a problem in not having separated out the global temperature vs the Urban Heat Island (UHI) effect. e.g., in equation (2). Could this affect the statistics?

See

Atmospheric Circulations do not Explain the Temperature-Industrialization Correlation Ross McKitrick (in press, 2010).

Beenstock and Reingewertz claim: “greenhouse gas forcings have a temporary effect on global temperature.” While they show temperature and greenhouse to have a different order, I don’t follow their inference that the CO2 effect is temporary. Though the incremental CO2 absorption is decreasing with increasing CO2 concentration does not mean the increase in CO2 absorption is temporary.

If the enormous ocean buffer was included, then I could see the CO2 described as “temporary”. However, they did not mention the ocean.

I guess it says thast the system has been fundamentally mischaracterized. What is called ‘model risk’.

I wonder the degree to which non-linearity can affect the signfiicance tests. Eg do such relationships as T=a+b*log(CO2) get excluded? And what is the role of problems with the temperature record?

The reliability of this approach can be checked simply by applying it to model data on global temperature trends with and without anthropogenic forcings. These are cited in the report of Working Group 1 of the IPCC and are easily available. Clearly, if this method does not find the effect of CO2 forcing in model outputs that explicitly include it, the method has a problem, not atmospheric science

Yes it would be worth doing this sort of reverse engineering, as it is doing system identification, it could be checked with a range of synthetic known systems.

General Circulation models are not “Atmospheric Science”.

Your suggestion, while good, must be noted as testing whether the “polynomial integration” method is a valid test of AGW, not whether AGW is right or not.

assuming the models are valid and able to predict the future climate reliably.

No, it doesn’t assume that. The models clearly include CO2 forcing – that’s essentially a matter of definition. If the analysis technique cannot discern that, then the analysis technique is flawed. It seems possible that the problem with the specific analysis done is that the temperature was correlated to the concentration of CO2, when the log of the concentration should have been used.

I think it's identical. Their statement on poly cointegrated is exactly their claim that GHG forcing is I(2), temp and solar are I(1). And “AGW is refuted” ~ “End of AGW” – what's the difference?

Nick: Copied from WUWTVS (02:39:23) :Dave Tufte (15:50:00) :Yes, you are right when you stress that the basic problem is that GHGâ€™s are I(2) and temperature is I(1). Asymptotically (if the sample size, n, goes to infinity) these two stochastic trends are independent.But then you state:â€œFirst, disregard the polynomial part. Thatâ€™s a modelling tweak that probably doesnâ€™t matter too much (if anything, it makes me think they fished a bit and thus doubt the conclusions).â€Beenstock and Reingewertz indeed use a â€˜model tweakâ€™ that would allow for these two series to be cointegrated on the next level. But that â€˜model tweakâ€™ is not in itself something trivial. Polynomial cointegration has first been described by Yoo (1986), and since then a solid body of literature has been developed on the topic, where contributors include the likes of Johansen (!) and Granger (!). This is the established way to deal with I(2)/I(1) relationships.So, the difference between Kaufmann et al (2006) and Beenstock and Reingewertz (2009) is the following:**Kaufmann et al (2006) attempt to cointegrate temperature, I(1) with the sum of radiative forcing, which is I(2) (equation (3), p. 255). This is plain wrong.**Beenstock and Reingewerts (2009) first cointegrate various greenhouse gases back to a I(1) variable, and then attempt to cointegrate temperature with this I(1) variable. This is the accurate approach.They find that solar irradiance is the most important factor determining temperature levels (what a surprise).â€œThis shows that the first differences of greenhouse gases are empirically important but not their levels. The most important variable is solar irradiance. Dropping this variable, but retaining the first differences of the greenhouse gas forcings, adversely affects all three cointegration test statisticsâ€They then proceed to show what happens if you ignore the different order of integration, like Kaufmann et al (2006) did.â€œHaldrupâ€™s (1994) critical value of the cointegration test statistic when there are three I(2) variables and two I(1) variables is about -4.25. Therefore equation (4) is clearly not polynomially cointegrated, and the conclusions of these studies regarding the effect of rfCO2 on global temperature are incorrect and spurious.â€Specifically, they argue that the following conclusion, by Kaufmann et al (2006) on p.255, is spurious:â€œThe ADF statistic strongly rejects (P < 0.01) the null hypothesis that the residual contains a stochastic trend, regardles of the lag length used in Equation (2) (Table I), which indicates that the variables in (3) cointegrate.”Let me stress the most important point here. By incorrectly applying these procedures Kaufmann et al. (2006) conclude that an increase in CO2 has a permanent effect on temperatures. Beenstock and Reingewerts (2009), by correctly applying the procedure, conclude that it is in fact only temporary.So, you are right to state that the variables being I(1) and I(2) respectively, is the main issue. However, the procedure described by Beenstock and Reingewerts (2009) is not just a 'model tweak'.

Stepping back here — what do they show? That an equilibrium exists between temperature and solar insolation, that an equilibrium exists between the GHGs, but there is no empirical equilibrium between the GHGs and temperature/solar insolation. That is, levels of GHG may drift arbitrarily far away from temperature over time. Not so temperature and solar. The geological record shows this, and they claim to show their stats show this in the timescale of the last century.

Nick: Copied from WUWT

VS (02:39:23) :

Dave Tufte (15:50:00) :

Yes, you are right when you stress that the basic problem is that GHG’s are I(2) and temperature is I(1). Asymptotically (if the sample size, n, goes to infinity) these two stochastic trends are independent.

But then you state:

“First, disregard the polynomial part. That’s a modelling tweak that probably doesn’t matter too much (if anything, it makes me think they fished a bit and thus doubt the conclusions).”

Beenstock and Reingewertz indeed use a ‘model tweak’ that would allow for these two series to be cointegrated on the next level. But that ‘model tweak’ is not in itself something trivial. Polynomial cointegration has first been described by Yoo (1986), and since then a solid body of literature has been developed on the topic, where contributors include the likes of Johansen (!) and Granger (!). This is the established way to deal with I(2)/I(1) relationships.

So, the difference between Kaufmann et al (2006) and Beenstock and Reingewertz (2009) is the following:

**Kaufmann et al (2006) attempt to cointegrate temperature, I(1) with the sum of radiative forcing, which is I(2) (equation (3), p. 255). This is plain wrong.

**Beenstock and Reingewerts (2009) first cointegrate various greenhouse gases back to a I(1) variable, and then attempt to cointegrate temperature with this I(1) variable. This is the accurate approach.

They find that solar irradiance is the most important factor determining temperature levels (what a surprise).

“This shows that the first differences of greenhouse gases are empirically important but not their levels. The most important variable is solar irradiance. Dropping this variable, but retaining the first differences of the greenhouse gas forcings, adversely affects all three cointegration test statistics”

They then proceed to show what happens if you ignore the different order of integration, like Kaufmann et al (2006) did.

“Haldrup’s (1994) critical value of the cointegration test statistic when there are three I(2) variables and two I(1) variables is about -4.25. Therefore equation (4) is clearly not polynomially cointegrated, and the conclusions of these studies regarding the effect of rfCO2 on global temperature are incorrect and spurious.”

Specifically, they argue that the following conclusion, by Kaufmann et al (2006) on p.255, is spurious:

“The ADF statistic strongly rejects (P < 0.01) the null hypothesis that the residual contains a stochastic trend, regardles of the lag length used in Equation (2) (Table I), which indicates that the variables in (3) cointegrate."

Let me stress the most important point here. By incorrectly applying these procedures Kaufmann et al. (2006) conclude that an increase in CO2 has a permanent effect on temperatures. Beenstock and Reingewerts (2009), by correctly applying the procedure, conclude that it is in fact only temporary.

So, you are right to state that the variables being I(1) and I(2) respectively, is the main issue. However, the procedure described by Beenstock and Reingewerts (2009) is not just a 'model tweak'.

Stepping back here — what do they show? That an equilibrium exists between temperature and solar insolation, that an equilibrium exists between the GHGs, but there is no empirical equilibrium between the GHGs and temperature/solar insolation. That is, levels of GHG may drift arbitrarily far away from temperature over time. Not so temperature and solar. The geological record shows this, and they claim to show their stats show this in the timescale of the last century.

General Circulation models are not “Atmospheric Science”.Your suggestion, while good, must be noted as testing whether the “polynomial integration” method is a valid test of AGW, not whether AGW is right or not.

“In short, they are testing a necessary, rather than sufficient, (statistical) conditions for causality. If you cannot detect a nudge in temperatures, on any level, due to CO2 forcing, then what on Earth is all the CO2 fuss about?”More from VS at WUWT. Verifies some of the results. Reviews the literature. Well worth a read.

“In short, they are testing a necessary, rather than sufficient, (statistical) conditions for causality. If you cannot detect a nudge in temperatures, on any level, due to CO2 forcing, then what on Earth is all the CO2 fuss about?”

More from VS at WUWT. Verifies some of the results. Reviews the literature. Well worth a read.

You might also like to check my query to VS/ So far, no answer. B&R talk a lot about CO2 etc being I(2), and how that is incompatible with temp being I(1). But there’s absolutely no proof that temp is I(1). It’s just dogma. There are no probability stats quoted, or error bars.

The critical thing is not just that temp is I(1), but that it isn’t I(2). Mostly people verify the minimum n only, as in, we know it’s not I(0) and it could be I(1). But the B&R conclusion requires absolutely that temp is I(1) and couldn’t have a significant I(2) component.

Nick. If the first difference is stationary, then all successive differences must be, I think. The I(1) of temperature is easily shown, as VS did earlier, I am sure there are references. I did in a post years ago asking is temperature a random walk http://landshape.org/enm/is-temperature-a-random-walk/?

There are issues though, as the post indicates. I think the way to say it is that the tests lack power. You can’t be sure, and breaks and long periodicity could affect it.

The I(1) of temperature is easily shown, as VS did earlier,Where? The nearest I could find was “I guess temperature is I(1), right?” But you are using the same dogmatism that B&R use. You can never say absolutely that temperature is I(1). You have a finite amount of data, and can only say with reference to probability stats and error bars.

Nowheredo B&R do this, and neither do you. And yes, if a series is exactly I(1), then so will be higher differences. But that’s unrealisable. With a finite series, the error bars widen with each differencing.Nick here:

VS (09:34:02) :@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.The ADF test is set up with an I(1) null, so the precise statement is that I(1) is not rejected. That is the error analysis. Perhaps your point is you want an I(1) alternate hypothesis?

While the difference between a fractionally differenced series of 0.98 and 1 is important asymptotically, i.e. I(1) goes to plus or minus infinity, and is worthy of testing (though I cant find any R tests), I think it does not make much difference to the article. Because the issue at heart is whether CO2 and Temperature are spuriously correlated, and both d=0.98 and d=1 are going to have high spurious correlation potential.

“the precise statement is that I(1) is not rejected”Thanks, I missed that VS post. But this imprecision is why I object to the dogmatic language. “we can’t say it isn’t I(1)” becomes “it is I(1)”, in the same way, CO2 “is I(2)”, and the two are said to be incompatible. Logically, when precisely stated, there’s no proof.

This is new to me, but from a brief scan of the subject, it looks like the analysis by B&R only applies to exactly unit roots for integer differences (0,1,2…). I see no reason to believe that temperature or CO2 has identically unit roots for any integer difference and so cannot be made stationary by differencing. Does that mean the analysis fails and the conclusion cannot be supported?

This is new to me, but from a brief scan of the subject, it looks like the analysis by B&R only applies to exactly unit roots for integer differences (0,1,2…). I see no reason to believe that temperature or CO2 has identically unit roots for any integer difference and so cannot be made stationary by differencing. Does that mean the analysis fails and the conclusion cannot be supported?

You might also like to check my query to VS/ So far, no answer. B&R talk a lot about CO2 etc being I(2), and how that is incompatible with temp being I(1). But there's absolutely no proof that temp is I(1). It's just dogma. There are no probability stats quoted, or error bars. The critical thing is not just that temp is I(1), but that it isn't I(2). Mostly people verify the minimum n only, as in, we know it's not I(0) and it could be I(1). But the B&R conclusion requires absolutely that temp is I(1) and couldn't have a significant I(2) component.

Nick. If the first difference is stationary, then all successive differences must be, I think. The I(1) of temperature is easily shown, as VS did earlier, I am sure there are references. I did in a post years ago asking is temperature a random walk http://landshape.org/enm/is-temperature-a-rando…There are issues though, as the post indicates. I think the way to say it is that the tests lack power. You can't be sure, and breaks and long periodicity could affect it.

The I(1) of temperature is easily shown, as VS did earlier,Where? The nearest I could find was “I guess temperature is I(1), right?” But you are using the same dogmatism that B&R use. You can never say absolutely that temperature is I(1). You have a finite amount of data, and can only say with reference to probability stats and error bars.Nowheredo B&R do this, and neither do you. And yes, if a series is exactly I(1), then so will be higher differences. But that's unrealisable. With a finite series, the error bars widen with each differencing.Nick here:

VS (09:34:02) :@Tom PI 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 < 0.2323Augmented 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 < 0.0000At first sight, temperature seems to be I(1), as the authors claim.The ADF test is set up with an I(1) null, so the precise statement is that I(1) is not rejected. That is the error analysis. Perhaps your point is you want an I(1) alternate hypothesis? While the difference between a fractionally differenced series of 0.98 and 1 is important asymptotically, i.e. I(1) goes to plus or minus infinity, and is worthy of testing (though I cant find any R tests), I think it does not make much difference to the article. Because the issue at heart is whether CO2 and Temperature are spuriously correlated, and both d=0.98 and d=1 are going to have high spurious correlation potential.Eg. http://www.informaworld.com/smpp/content~conten…AbstractThis paper argues that the predominant method of estimating equilibrium relationships in macroeconometric models, namely the VECM system of Johansen, is severely flawed if the underlying variables are distributed as near unit root processes. Researchers may apply cointegration techniques to these processes, as the power of rejecting near unit roots using standard unit root tests is extremely low. Using Monte Carlo analysis, problematic behaviour of cointegration analysis is found in detecting the true underlying form of the connection between the near unit root processes. Furthermore the connecting vector is imprecisely estimated, resulting in problematic inference for error correction models.

“the precise statement is that I(1) is not rejected”Thanks, I missed that VS post. But this imprecision is why I object to the dogmatic language. “we can't say it isn't I(1)” becomes “its is I(1)”, in the same way, CO2 “is I(2)”, and the two are said to be incompatible. Logically, when precisely stated, there's no proof.Here's another paper about cointegration and near unit root processes:http://www.federalreserve.gov/pubs/ifdp/2007/90…Abstract:Methods of inference based on a unit root assumption in the data are typically not robust to even small deviations from this assumption. In this paper, we propose robust procedures for a residual-based test of cointegration when the data are generated by a near unit root process. ABonferroni method is used to address the uncertainty regarding the exact degree of persistence in the process. We thus provide a method for valid inference in multivariate near unit root processes where standard cointegration tests may be subject to substantial size distortions and standard OLS inference may lead to spurious results. Empirical illustrations are given by: (i) a re-examination of the Fisher hypothesis, and (ii) a test of the validity of the cointegrating relationship between aggregate consumption, asset holdings, and labor income, which has attracted a great deal of attention in the recent fiÂ…nance literature.

Eg. http://www.informaworld.com/smpp/content~content=a713692127&db=all

Abstract

This paper argues that the predominant method of estimating equilibrium relationships in macroeconometric models, namely the VECM system of Johansen, is severely flawed if the underlying variables are distributed as near unit root processes. Researchers may apply cointegration techniques to these processes, as the power of rejecting near unit roots using standard unit root tests is extremely low. Using Monte Carlo analysis, problematic behaviour of cointegration analysis is found in detecting the true underlying form of the connection between the near unit root processes. Furthermore the connecting vector is imprecisely estimated, resulting in problematic inference for error correction models.

Here’s another paper about cointegration and near unit root processes:

http://www.federalreserve.gov/pubs/ifdp/2007/907/ifdp907.pdf

Abstract:

Methods of inference based on a unit root assumption in the data are typically not robust to even small deviations from this assumption. In this paper, we propose robust procedures for a residual-based test of cointegration when the data are generated by a near unit root process. A Bonferroni method is used to address the uncertainty regarding the exact degree of persistence in the process. We thus provide a method for valid inference in multivariate near unit root processes where standard cointegration tests may be subject to substantial size distortions and standard OLS inference may lead to spurious results. Empirical illustrations are given by: (i) a re-examination of the Fisher hypothesis, and (ii) a test of the validity of the cointegrating relationship between aggregate consumption, asset holdings, and labor income, which has attracted a great deal of attention in the recent finance literature.

I read it. It says the cointegration tests will tend of over-reject if there is a small deviation from the unit root. Might be a problem then. But Beenstock uses a number of tests. Not clear. Should ask him.

I read it. It says the cointegration tests will tend of over-reject if there is a small deviation from the unit root. Might be a problem then. But Beenstock uses a number of tests. Not clear. Should ask him.

Still an interesting approach, but could use more qualification. Have started getting code together for the tests.

Still an interesting approach, but could use more qualification. Have started getting code together for the tests.

Something I would like to see would be to take a known I(2) time series with 120 points (y=t^2 + a) with the range of y equal to the range of the temperature anomaly from 1880 to 200x) and add more and more noise to see what level of noise is required for the first difference of the time series to fail the unit root test. Then see what the data looks like compared to the temperature data.

I would like to see a range of sensitivity tests too. I think I will

be looking into cointegration and into this paper in more detail in

the coming weeks.

Beenstock and Reingewertz are using a too short forcing record which biases their test for a hinged forcing (two straight lines). If you look at the NOAA AGGI, which is the best record of forcings since 1979, it is clearly linear, and the IPCC discussion shows historical forcings are pretty clearly hinged.This is a somewhat more sophisticated version of chiefio, where someone without the background assumes things that just ain't so.

Something I would like to see would be to take a known I(2) time series with 120 points (y=t^2 + a) with the range of y equal to the range of the temperature anomaly from 1880 to 200x) and add more and more noise to see what level of noise is required for the first difference of the time series to fail the unit root test. Then see what the data looks like compared to the temperature data.

Beenstock and Reingewertz are using a too short forcing record which biases their test for a hinged forcing (two straight lines). If you look at the NOAA AGGI, which is the best record of forcings since 1979, it is clearly linear, and the IPCC discussion shows historical forcings are pretty clearly hinged.

This is a somewhat more sophisticated version of chiefio, where someone without the background assumes things that just ain’t so.

Dont follow your logic here. B&R say they use GISS data, which

starts around 1880. The break they discuss is in 1964, prior to 1979,

so being linear since then is not the issue. B&R are in agreement

with IPCC there seems that there is a hinge. They then use a test to

reject the hypothesis that rfCO2 is I(1) with a break, and so

eliminate the possible confounding effect.

The GISS papers they point to are for temperature, not radiative forcing. They say there APPEARS to be a hinge, but they reject that based on the CMR test and say that the forcing is order two

I had a look at your post on it. You seem to be confusing I(n) and

X^n. They are completely different things.

Even if statistically the increase in global avg temp would not be distinguishable from a ‘random walk’, physically it doesn’t make a lot of sense: Conservation of energy would push temperatures back to equilibrium. Unles of course there’s a forcing acting upon the climate system, which indeed there is (enhanced GHG concentrations being the major one).

See also

http://ourchangingclimate.wordpress.com/2010/03/08/is-the-increase-in-global-average-temperature-just-a-random-walk/

and a lengthy discussion in the preceding thread.

That temperature is not asymptopically a random walk does not worry me too much. All model disagree with assumptions to some extent eg linearizations, simplifications. You have to also take into account that temperature inherits a great deal of its properties from the solar insolation. You also have the positive feedbacks that reduce ‘push back’ within the bounds we are looking at.

So the objection that ‘T is not a random walk because it is not unbounded’ is not a big problem for the approach.

I would like to see a range of sensitivity tests too. I think I willbe looking into cointegration and into this paper in more detail inthe coming weeks.

Dont follow your logic here. B&R say they use GISS data, whichstarts around 1880. The break they discuss is in 1964, prior to 1979,so being linear since then is not the issue. B&R are in agreementwith IPCC there seems that there is a hinge. They then use a test toreject the hypothesis that rfCO2 is I(1) with a break, and soeliminate the possible confounding effect.

The GISS papers they point to are for temperature, not radiative forcing. They say there APPEARS to be a hinge, but they reject that based on the CMR test and say that the forcing is order two

I had a look at your post on it. You seem to be confusing I(n) andX^n. They are completely different things.

Even if statistically the increase in global avg temp would not be distinguishable from a 'random walk', physically it doesn't make a lot of sense: Conservation of energy would push temperatures back to equilibrium. Unles of course there's a forcing acting upon the climate system, which indeed there is (enhanced GHG concentrations being the major one). See alsohttp://ourchangingclimate.wordpress.com/2010/03…and a lengthy discussion in the preceding thread.

That temperature is not asymptopically a random walk does not worry me too much. All model disagree with assumptions to some extent eg linearizations, simplifications. You have to also take into account that temperature inherits a great deal of its properties from the solar insolation. You also have the positive feedbacks that reduce 'push back' within the bounds we are looking at. So the objection that 'T is not a random walk because it is not unbounded' is not a big problem for the approach.

assuming the models are valid and able to predict the future climate reliably.

No, it doesn't assume that. The models clearly include CO2 forcing – that's essentially a matter of definition. If the analysis technique cannot discern that, then the analysis technique is flawed. It seems possible that the problem with the specific analysis done is that the temperature was correlated to the concentration of CO2, when the log of the concentration should have been used.

assuming the models are valid and able to predict the future climate reliably.

No, it doesn't assume that. The models clearly include CO2 forcing – that's essentially a matter of definition. If the analysis technique cannot discern that, then the analysis technique is flawed. It seems possible that the problem with the specific analysis done is that the temperature was correlated to the concentration of CO2, when the log of the concentration should have been used.