Talk:Cointegration

Untitled
A stock price and the dividend yield are not going to be cointegrated unless the dividend sequence is a stationary series. I would consider this to be quite unlikely from simple casual empiricism.

On the other hand, the basis on a stock futures contract would most likely be stationary. Feel free to revert the topic if you like but I think I'm right here. — Preceding unsigned comment added by 217.158.177.18 (talk) 18:17, 23 May 2005


 * Hi,


 * Thanks for contributing. You will acknowledge that the hypothesis of dividend->price connection could be (and has been) tested using cointegration techniques (whether or not they really are cointegrated). I will never revert an edit, especially a constructive one like this.
 * You may well have spotted an important error in communicating the idea, in that dividends and prices are not obviously cointegrated. However, I would say that futures and spot prices are so clearly cointegrated that we create another source of confusion; people could ask themselves, what the value of the method is (if it can only be used to prove relationships which are already enforced by arbitrage). I think the ideal example(s) would be less obvious than price-future, but more obvious than price-dividend.
 * What we really need is a case in which cointegration techniques proved their value against earlier econometrics, in an easy to describe way.
 * Any ideas?

Wragge 19:47, 2005 May 23 (UTC)


 * 1st sentence: it's not a "technique" any more than correlation is a technique. it's a "property" ... where the difference between two non-stationary series may itself be stationary. Derex 22:26, 18 January 2006 (UTC)

I(1)
From the intro: "Cointegration is a statistical property of a collection (X1,X2,...,Xk) of time series variables. First, all of the series must be integrated of order 1 (see Order of Integration). Next, if a linear combination of this collection is integrated of order zero, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order 1, and there exist coefficients a,b,c such that aX+bY+cZ is integrated of order 0, then X,Y, and Z are cointegrated."

From the actual Engle & Granger paper: "DEFINITION: The components of the vector xt are said to be co-integrated of order d, b, denoted xt ~ CI(d, b), if (i) all components of xt are I(d); (ii) there exists a vector a !=0 so that zt=a'xt-I(d -b), b>0. The vector a is called the co-integrating vector." Nowhere in here, Engle & Granger make a statement that "all of the series must be integrated of order 1 ". It is possible to have cointegration with higher order of integration as well. — Preceding unsigned comment added by 132.230.239.137 (talk) 14:35, 15 May 2016 (UTC)

De-trended?
I wonder about the line "Before the 1980s many economists used linear regressions on (de-trended) non-stationary time series data, ... showed to be a dangerous approach ..." Doesn't spurious correlation arise when you are using non-stationary data? If they used de-trended data then their data would be stationary (even if they de-trended it erroneously); thus, cannot be spuriously correlated, just badly correlated. However, if Granger says so, then I will definitely take his word for it. Therefore, I would like a reference on the word "de-trended". Ikiwi (talk) 13:25, 7 June 2011 (UTC)


 * No, if they detrended the data erroneously (and simply using the residuals from a regression of the data on time is sometimes erroneous) then the detrended data are not stationary. That's what is meant by erroneously in this context. That is the criticism that gave rise to cointegration tests. Duoduoduo (talk) 20:31, 6 January 2013 (UTC)

Criticism added
So I never heard about cointegration-type techniques until today and I'm sorry to say, to a mathematician, it looks like pure baloney. I added a criticism section with a link to a journal I found criticizing it. Please feel free to embellish this or maybe add some studies with empirical evidence showing that these kinds of techiques aren't just meaninglessly playing games with numbers (I'd like to see those). Maybe it would help if you could explain in the article whether this is meant to be a scientific technique or just a forecasting trick that might or might not work. Thanks. Doubledork (talk) 21:11, 3 January 2013 (UTC)


 * No, it's a legitimate feature of statistical analysis. I'm hazy on the details, but the basic idea is that if you regress y on x even though they are not cointegrated, then some types of hypothesis testing techniques are invalid because the residuals are not stationary.


 * Could someone who knows in detail about this put in some clarifications about why the concept of cointegration is important? Duoduoduo (talk) 20:18, 6 January 2013 (UTC)


 * It is important to model e.g. equilibrium relations. On a related note, to the Internet-acknowledged mathematician noting how the concept would be "balleney", it is always funny how random people in the Internet refute Nobel laureates (Engle and Granger partially won their price from cointegration). Maybe you'll come back after reading even the introductory textbooks, e.g. Lutkepohl, H. (2005): New Introduction to Multiple Time Series Analysis (Springer-Verlag); Hamilton, J. (1994): Time Series Analysis (Princeton University Press); Juselius, K.: (2006): The Cointegrated VAR-model (Oxford University Press), inter alia. I am just a random commenter like rest of you, but after reading some of the pages on econometrics, I find it extremely funny that some people have this weird agenda against the discipline, which has fundamentally influenced many other branches of science and particularly time series analysis. And which, I might add, has very little do to with economics per se. Thus, I propose a new Wikipedia-page: "why some random Internet-people insist on putting a criticism-section to every page". — Preceding unsigned comment added by 83.150.88.127 (talk) 12:33, 12 May 2013 (UTC)


 * I still think a big fat warning label is warranted in the article. Also, I refer you to the famous J. Scott Armstrong: "Certain hypotheses about econometric methods have been accepted for years despite the lack of evidence. Ninety-five percent of the experts agreed that econometric methods are superior for short-range forecasting. An examination of the empirical literature did not support this belief: Econometric forecasts were not shown to be significantly better in any of the 14 ex post and 16 ex ante tests. Furthermore, there was no tendency toward greater accuracy over these 30 tests. Similarly, 72% of the experts felt that complexity contributed to accuracy, but the examination of the literature did not support such a belief: Complex models were not significantly better in any of the five indirect and 11 direct tests." - from http://works.bepress.com/j_scott_armstrong/46/ and http://repository.upenn.edu/cgi/viewcontent.cgi?article=1008&context=marketing_papers Doubledork (talk) 19:33, 8 January 2013 (UTC)

Cointelation?
This article makes it sounds like cointelation is a widely accepted alternative to cointegration. However, the only reference I can find to cointelation is the 2012 article that is cited in this wikipedia page. Did the authors of the 2012 cointelation article update this part of the wiki themselves? Since this method is not widely used and does not constitute a major advance in econometrics, I highly doubt it belongs on the cointegration wiki page. — Preceding unsigned comment added by 18.111.26.23 (talk) 20:23, 17 February 2013 (UTC)


 * Yeah. Never heard of it either. Does not appear in any notable journal of statistics, econometrics, or mathematics. Typical Wikipedia cra*. — Preceding unsigned comment added by 83.150.88.127 (talk) 12:43, 12 May 2013 (UTC)


 * Agreed 94.100.23.163 (talk) 07:53, 30 May 2013 (UTC)

Major Edit
Made some major edits, moving most things about and hopefully clarifying things. I'm not an econometrician, but I have a) some mid-level stats training and b) some experience teaching stats to people who are unfamiliar with them. Theblindsage (talk) 22:30, 5 May 2015 (UTC)

Common Confusion
I have deleted this comment from the last part of HISTORY and replaced by more accurate description:

—even though there is no direct relationship between the two series and hence the high correlation between the two series is probably caused by ″global″ economic factors that affect both countries, an uncareful reading of the regression results could lead to the misinterpretation of a strong direct relationship between the two series. The R-square will typically be much lower if we regress across the time series of returns between one Fiji consumption level and the next (verus returns in the Afgan GNP), but subtle spurious regression may remain.

This passage reflects the common misunderstanding that if there is correlation it must be for a cause -- if the two series are not related than there is some global economic factor which makes them appear related. SPURRIOUS means that there is a correlation but there is no cause -- that is why it is spurious.Asaduzaman (talk) 14:10, 24 October 2015 (UTC)

Dr. Chen's comment on this article
Dr. Chen has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"In my opinion the article is well written. All key ideas on cointegration are included. I would also include the Johanson paper (Johansen, Søren (1991). "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models". Econometrica 59 (6): 1551–1580. JSTOR 2938278.) in the reference list, though a link to the Johanson test is given in the article."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Chen has published scholarly research which seems to be relevant to this Wikipedia article:


 * Reference : Chen Pu & Hsiao Chihying, 2005. "Testing Cointegration Rank in Large Systems," Econometrics 0504002, EconWPA.

ExpertIdeasBot (talk) 23:38, 19 May 2016 (UTC)

Dr. Lutkepohl's comment on this article
Dr. Lutkepohl has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"The general introduction is fine. I propose a couple of changes/corrections below because I think that the common trends property of cointegrated variables needs to be emphasized more. In my view Sec 2 on Tests is not very informative and as it stands even misleading. So it should be deleted. First, the Engle-Granger method is ok if one considers only two variables. The description is not very informative, however. The same is true for the descriptions of the other tests. The comments on the Johansen test are even misleading. In fact, from what is explained in the introduction to the item it is clear that cointegration is a systems property. Hence, cointegration tests should be done in a systems context and in my reading of the literature that is in fact understood and done by practitioners. Hence, the Johansen type tests or related tests derived in a systems context are the common tests today. Since the intuition behind these tests may not be easy to explain to a general audience it may be best to refer readers to the relevant literature, in particular, Johansen, S. (1995), Likelihood-based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press and/or textbook expositions in Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press, Lütkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, Springer and the textbooks listed under ‘Further reading’.

Most of the references given for this item are rather special articles and hardly recommended reading for a general audience looking for an introduction to the topic (e.g., [4], [7], [8], [9], [10], [11]). Suggested changes for introductory part: Replace ‘They also showed that unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them.’ by ‘Cointegrated time series share a common trend and thus have a strong relation. Unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them.’

Replace ‘form a stationary linear combination of them. For instance, a stock market index’ by ‘form a stationary linear combination of them. In that case the series are driven by the same stochastic trend. For instance, a stock market index’"

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Lutkepohl has published scholarly research which seems to be relevant to this Wikipedia article:


 * Reference : Markku Lanne & Helmut Luetkepohl & Katarzyna Maciejowska, 2009. "Structural Vector Autoregressions with Markov Switching," Economics Working Papers ECO2009/06, European University Institute.

ExpertIdeasBot (talk) 09:20, 16 June 2016 (UTC)

Dr. Dreger's comment on this article
Dr. Dreger has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"First paragraph: Not all time series need to share the same order of integration. At least, two time series should share the highest order of integration, say d and a linear combination of them should have an order of d-1. Example: If the series are I(1) and cointegrated, the residual arising from the linear combination is I(0), i.e. stationary. There is no need to restrict the concept to I(1) variables, series might be also I(2). If these series are cointegrated, the residuals might be either I(1) or I(0). Similarly, an I(2) series (such as the capital stock) has two unit roots.

Johansen test: I would delete the sentence "This test is subject to asymptotic properties ...". This requirement is also relevant for the unit root tests mentioned above. In addition, it is not bad to have as much observations as possible for the ARDL test. As a further advantage of the Johansen test, the a priori distinction between endogenous and exogenous variables is not necessary."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Dreger has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference : Dreger, Christian & Wolters, Jurgen, 2011. "Money and inflation in the euro area during the financial crisis," Discussion Papers 300, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.

ExpertIdeasBot (talk) 19:53, 1 July 2016 (UTC)

Dr. Johansen's comment on this article
Dr. Johansen has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"This is highly problematic. The definition in line 1 is not one that is now the basis for the theory of cointegration, but is a repeat of a preliminary definition from the Engle-Granger 1987 paper. The choice of topics reveals that the author has never done a serious application of cointegration, and one gets the suspicion that the purpose of the note is selfpromotion. The choice of topics i peculiar, and the choice of references strange. I am not sure what happens if one writes something else. Will the author not just change it again? What are the rules? If I remember correctly, Peter Reinhard Hansen had a contribution to Wikipedia on cointegration. Is that still there? Other possibilities are Bent Nielsen (Nuffield Oxford) or Brendan Beare ( San Diego)"

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Johansen has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference : Sren Johansen, 2007. "Some Identification Problems in the Cointegrated Vector Autoregressive Model," Discussion Papers 07-24, University of Copenhagen. Department of Economics.

ExpertIdeasBot (talk) 16:24, 11 July 2016 (UTC)

Dr. Fachin's comment on this article
Dr. Fachin has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"the article does not contain any actual mistakes, but overall it is pretty confused. I will try to edit it myself"

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Fachin has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference 1: Francesca Di Iorio & Stefano Fachin, 2014. "Dealing with unobservable common trends in small samples: a panel cointegration approach," DSS Empirical Economics and Econometrics Working Papers Series 2014/5, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.


 * Reference 2: Francesca DI IORIO & Stefano FACHIN & Riccardo LUCCHETTI, 2013. "Can you do the wrong thing and still be right? Hypothesis Testing in I(2) and near-I(2) cointegrated VARs," Working Papers 395, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

ExpertIdeasBot (talk) 16:28, 11 July 2016 (UTC)

Dr. Destefanis's comment on this article
Dr. Destefanis has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"This is by far the worst article of the batch. I wonder if I could get from it what cointegration is about without any previous knowledge. These are two helpful references: https://www.quora.com/What-is-cointegration-of-time-series-data-in-statistics; http://www.rimini.unibo.it/fanelli/Hendry-Juselius-part1.pdf (more highbrow); http://www.rimini.unibo.it/fanelli/Hendry-Juselius-part2.pdf (definitely more highbrow)."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Destefanis has expertise on the topic of this article, since he has published relevant scholarly research:


 * Reference : Roberto Basile & Mauro Costantini & Sergio Destefanis, 2005. "Unit root and cointegration tests for cross-sectionally correlated panels. Estimating regional production functions," CELPE Discussion Papers 94, CELPE - Centre of Labour Economics and Economic Policy, University of Salerno, Italy.

ExpertIdeasBot (talk) 16:37, 2 August 2016 (UTC)

typo wrt beta?
In the paragraph under tests:

" If we knew $$u_t$$, we could just test it for stationarity with something like a Dickey–Fuller test, Phillips–Perron test and be done. But because we don't know $$u_t$$, we must estimate this first, generally by using ordinary least squares, and then run our stationarity test on the estimated $$u_t$$ series, often denoted $$\hat{u}_t$$. "

Shouldn't $$u_t$$ be $$\beta$$? Then the estimation of $$\beta$$ ( $$\hat{\beta}$$ ?) by regression gives $$\hat{u}_t$$.

Engle-Granger two-step method needs more detail
In the section explaining the Engle-Granger method, it states "A second regression is then run on the first differenced variables from the first regression, and the lagged residuals ${\hat {u}}_ $ is included as a regressor.
 * undefined"

However, this needs to be explained in more detail, displaying the regression equation, and should mention the lagged residuals $$\sum_{i=1}^n \Delta u_{t-i}$$ which are there to correct for serial correlation.

I'm not experienced in this, so I can't add this myself. But I saw this mentioned at 3:15 at https://www.youtube.com/watch?v=q5wbOSjbVW4 and in equation 4, page 506 of https://www.jstor.org/stable/1926789.