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unstable cointegration vector estimates in Johansen test
6 messages · Charles Evans, Eric Zivot, Matthieu Stigler +1 more
Hello Paul (Lestat?!?), In my work, I have looked at potential cointegration between certain categories of ETFs and the most nearly related futures, and I have found wide disagreement among different cointegration tests. Different cointegration tests have different strengths and weaknesses. Because there is rarely a conclusive reason to prefer any particular cointegration test over all others. Optimally, one would use a variety (e.g., Engle-Granger/ADF, Engle-Granger/Phillips-Perron, ECM, Phillips-Ouliaris [ca.po], Johansen [ca.jo]) and run with the consensus. Although it could be a bit tedious, you could run your rolling cointegration tests using each of these and see if you get the same odd behavior consistently. If you do, then that would suggest something interesting; if not, then it could just be an artifact of the specific test. If you have access to statistics and econometrics journals, you might find these papers helpful: Gregory, Allan W., Alfred A. Haug, and Nicoletta Lomuto, 2004, Mixed signals among tests for cointegration. Journal of Applied Econometrics 19 (1), 89-98. Hanck, Christoph, 2007, Mixed signals among panel cointegration tests. Working Paper. https://editorialexpress.com/cgibin/conference/download.cgi?db_name=sce2007&paper_id=115 Haug, Alfred A., 1996, Tests for cointegration: A Monte Carlo comparison. Journal of Econometrics 71, 89-115. ?stermark, Ralf and Rune H?glund, 2000. Monte Carlo tests of cointegration with structural breaks. Kybernetes 29 (9/10), 1284-1297. ?stermark, Ralf and Rune H?glund, 1999. Simulating competing cointegration tests in a bivariate system. Journal of Applied Statistics 27 (7), 831-846. HTH, Charles Evans cevans at chyden.net No one ever says, "First shoot all the plumbers." Steve Foerster
On 1 Dec 2010, at 5:45 PM, ??? wrote:
Hi, all, a question regarding the cointegration relations (vectors) estimate in the Johansen test: I have a data sample which is confirmed by the Johansen test as cointegrated, however, if I take a subsample of the whole times series, each time add one data point and using the "ca.jo" function in R to estimate the cointegrating vector, i.e. to do a forward recursive test, and record the estimate beta (the first element of the vector is normalized to one, beta is the second element), strangely at some point, beta shows discontinuity-a big jump with sign change. This is really confusing to me as it seems that the Johansen procedure is not robust in that one additional data could cause dramatical change in the estimate of beta. not sure if it is problem of the procedure or the ca.jo function, I think my data is fine (excluding errors and outliers). has anyone seen similar things as me? Regards, Paul C. Jin [[alternative HTML version deleted]]
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
Hi Besides the problem of different results based on different estimators, the fact that when doing a rolling analysis you find very different values with the same estimator could be due to a strange finite sample property of the ML estimator. Philips (ref below) finds indeed that in small samples the ML estimator has no finite moments, what can explain that single value have important impacts. See: Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January. http://ideas.repec.org/a/ecm/emetrp/v62y1994i1p73-93.html Best Matthieu Le 02. 12. 10 16:33, Charles Evans a ?crit :
Hello Paul (Lestat?!?), In my work, I have looked at potential cointegration between certain categories of ETFs and the most nearly related futures, and I have found wide disagreement among different cointegration tests. Different cointegration tests have different strengths and weaknesses. Because there is rarely a conclusive reason to prefer any particular cointegration test over all others. Optimally, one would use a variety (e.g., Engle-Granger/ADF, Engle-Granger/Phillips-Perron, ECM, Phillips-Ouliaris [ca.po], Johansen [ca.jo]) and run with the consensus. Although it could be a bit tedious, you could run your rolling cointegration tests using each of these and see if you get the same odd behavior consistently. If you do, then that would suggest something interesting; if not, then it could just be an artifact of the specific test. If you have access to statistics and econometrics journals, you might find these papers helpful: Gregory, Allan W., Alfred A. Haug, and Nicoletta Lomuto, 2004, Mixed signals among tests for cointegration. Journal of Applied Econometrics 19 (1), 89-98. Hanck, Christoph, 2007, Mixed signals among panel cointegration tests. Working Paper. https://editorialexpress.com/cgibin/conference/download.cgi?db_name=sce2007&paper_id=115 Haug, Alfred A., 1996, Tests for cointegration: A Monte Carlo comparison. Journal of Econometrics 71, 89-115. ?stermark, Ralf and Rune H?glund, 2000. Monte Carlo tests of cointegration with structural breaks. Kybernetes 29 (9/10), 1284-1297. ?stermark, Ralf and Rune H?glund, 1999. Simulating competing cointegration tests in a bivariate system. Journal of Applied Statistics 27 (7), 831-846. HTH, Charles Evans cevans at chyden.net No one ever says, "First shoot all the plumbers." Steve Foerster On 1 Dec 2010, at 5:45 PM, ??? wrote:
Hi, all,
a question regarding the cointegration relations (vectors) estimate
in the
Johansen test:
I have a data sample which is confirmed by the Johansen test as
cointegrated, however, if I take a subsample of the whole times
series, each
time add one data point and using the "ca.jo" function in R to
estimate the
cointegrating vector, i.e. to do a forward recursive test, and record
the
estimate beta (the first element of the vector is normalized to one,
beta is
the second element), strangely at some point, beta shows
discontinuity-a big
jump with sign change. This is really confusing to me as it seems
that the
Johansen procedure is not robust in that one additional data could cause
dramatical change in the estimate of beta. not sure if it is problem
of the
procedure or the ca.jo function, I think my data is fine (excluding
errors
and outliers). has anyone seen similar things as me?
Regards,
Paul C. Jin
[[alternative HTML version deleted]]
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
The situation is even worse, because rolling estimates are correlated as well. Because the finite sample distn has no moments, you expect to see crazy results from the Johansen MLE from time to time. I have certainly seen estimates that are 10,000 when they should be near 1. This of course, makes it very difficult to judge the stability of recursive or rolling MLEs. Because the Stock-Watson DOLS estimates are regression they will be more stable. Still it would be nice to have some distribution theory for moving estimates of a cointegrating vector. Banerjee, Lumsdain and Stock has a JBES 1992 paper that derived the distn of rolling and recursive unit root tests. It would be nice to know if such an analysis has been done for cointegration. Eric Zivot Robert Richards Chaired Professor of Economics Adjunct Professor of Finance Adjunct Professor of Statistics Department of Economics Box 353330 email: ezivot at u.washington.edu University of Washington phone: 206-543-6715 Seattle, WA 98195-3330 www: http://faculty.washington.edu/ezivot -----Original Message----- From: r-sig-finance-bounces at r-project.org [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of mat Sent: Friday, December 03, 2010 2:53 AM To: r-sig-finance at r-project.org Subject: Re: [R-SIG-Finance] unstable cointegration vector estimates in Johansen test Hi Besides the problem of different results based on different estimators, the fact that when doing a rolling analysis you find very different values with the same estimator could be due to a strange finite sample property of the ML estimator. Philips (ref below) finds indeed that in small samples the ML estimator has no finite moments, what can explain that single value have important impacts. See: Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January. http://ideas.repec.org/a/ecm/emetrp/v62y1994i1p73-93.html Best Matthieu Le 02. 12. 10 16:33, Charles Evans a ?crit :
Hello Paul (Lestat?!?), In my work, I have looked at potential cointegration between certain categories of ETFs and the most nearly related futures, and I have found wide disagreement among different cointegration tests. Different cointegration tests have different strengths and weaknesses. Because there is rarely a conclusive reason to prefer any particular cointegration test over all others. Optimally, one would use a variety (e.g., Engle-Granger/ADF, Engle-Granger/Phillips-Perron, ECM, Phillips-Ouliaris [ca.po], Johansen [ca.jo]) and run with the consensus. Although it could be a bit tedious, you could run your rolling cointegration tests using each of these and see if you get the same odd behavior consistently. If you do, then that would suggest something interesting; if not, then it could just be an artifact of the specific test. If you have access to statistics and econometrics journals, you might find these papers helpful: Gregory, Allan W., Alfred A. Haug, and Nicoletta Lomuto, 2004, Mixed signals among tests for cointegration. Journal of Applied Econometrics 19 (1), 89-98. Hanck, Christoph, 2007, Mixed signals among panel cointegration tests. Working Paper. https://editorialexpress.com/cgibin/conference/download.cgi?db_name=sce2007&paper_id=115 Haug, Alfred A., 1996, Tests for cointegration: A Monte Carlo comparison. Journal of Econometrics 71, 89-115. ?stermark, Ralf and Rune H?glund, 2000. Monte Carlo tests of cointegration with structural breaks. Kybernetes 29 (9/10), 1284-1297. ?stermark, Ralf and Rune H?glund, 1999. Simulating competing cointegration tests in a bivariate system. Journal of Applied Statistics 27 (7), 831-846. HTH, Charles Evans cevans at chyden.net No one ever says, "First shoot all the plumbers." Steve Foerster On 1 Dec 2010, at 5:45 PM, ??? wrote:
Hi, all,
a question regarding the cointegration relations (vectors) estimate
in the
Johansen test:
I have a data sample which is confirmed by the Johansen test as
cointegrated, however, if I take a subsample of the whole times
series, each
time add one data point and using the "ca.jo" function in R to
estimate the
cointegrating vector, i.e. to do a forward recursive test, and record
the
estimate beta (the first element of the vector is normalized to one,
beta is
the second element), strangely at some point, beta shows
discontinuity-a big
jump with sign change. This is really confusing to me as it seems
that the
Johansen procedure is not robust in that one additional data could cause
dramatical change in the estimate of beta. not sure if it is problem
of the
procedure or the ca.jo function, I think my data is fine (excluding
errors
and outliers). has anyone seen similar things as me?
Regards,
Paul C. Jin
[[alternative HTML version deleted]]
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
1 day later
Depending on what the goal of the analysis is, but if the goal is to examine parameter stability, there is a recent nice paper that allows "time varying" cointegration (estimated by the Johansen ML): http://ideas.repec.org/a/cup/etheor/v26y2010i05p1453-1490_99.html I used this method, and the code will be available (hopefully) soon in package tsDyn. Best Matthieu Le 03. 12. 10 18:26, Eric Zivot a ?crit :
The situation is even worse, because rolling estimates are correlated as well. Because the finite sample distn has no moments, you expect to see crazy results from the Johansen MLE from time to time. I have certainly seen estimates that are 10,000 when they should be near 1. This of course, makes it very difficult to judge the stability of recursive or rolling MLEs. Because the Stock-Watson DOLS estimates are regression they will be more stable. Still it would be nice to have some distribution theory for moving estimates of a cointegrating vector. Banerjee, Lumsdain and Stock has a JBES 1992 paper that derived the distn of rolling and recursive unit root tests. It would be nice to know if such an analysis has been done for cointegration. Eric Zivot Robert Richards Chaired Professor of Economics Adjunct Professor of Finance Adjunct Professor of Statistics Department of Economics Box 353330 email: ezivot at u.washington.edu University of Washington phone: 206-543-6715 Seattle, WA 98195-3330 www: http://faculty.washington.edu/ezivot -----Original Message----- From: r-sig-finance-bounces at r-project.org [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of mat Sent: Friday, December 03, 2010 2:53 AM To: r-sig-finance at r-project.org Subject: Re: [R-SIG-Finance] unstable cointegration vector estimates in Johansen test Hi Besides the problem of different results based on different estimators, the fact that when doing a rolling analysis you find very different values with the same estimator could be due to a strange finite sample property of the ML estimator. Philips (ref below) finds indeed that in small samples the ML estimator has no finite moments, what can explain that single value have important impacts. See: Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January. http://ideas.repec.org/a/ecm/emetrp/v62y1994i1p73-93.html Best Matthieu Le 02. 12. 10 16:33, Charles Evans a ?crit :
Hello Paul (Lestat?!?), In my work, I have looked at potential cointegration between certain categories of ETFs and the most nearly related futures, and I have found wide disagreement among different cointegration tests. Different cointegration tests have different strengths and weaknesses. Because there is rarely a conclusive reason to prefer any particular cointegration test over all others. Optimally, one would use a variety (e.g., Engle-Granger/ADF, Engle-Granger/Phillips-Perron, ECM, Phillips-Ouliaris [ca.po], Johansen [ca.jo]) and run with the consensus. Although it could be a bit tedious, you could run your rolling cointegration tests using each of these and see if you get the same odd behavior consistently. If you do, then that would suggest something interesting; if not, then it could just be an artifact of the specific test. If you have access to statistics and econometrics journals, you might find these papers helpful: Gregory, Allan W., Alfred A. Haug, and Nicoletta Lomuto, 2004, Mixed signals among tests for cointegration. Journal of Applied Econometrics 19 (1), 89-98. Hanck, Christoph, 2007, Mixed signals among panel cointegration tests. Working Paper. https://editorialexpress.com/cgibin/conference/download.cgi?db_name=sce2007&paper_id=115 Haug, Alfred A., 1996, Tests for cointegration: A Monte Carlo comparison. Journal of Econometrics 71, 89-115. ?stermark, Ralf and Rune H?glund, 2000. Monte Carlo tests of cointegration with structural breaks. Kybernetes 29 (9/10), 1284-1297. ?stermark, Ralf and Rune H?glund, 1999. Simulating competing cointegration tests in a bivariate system. Journal of Applied Statistics 27 (7), 831-846. HTH, Charles Evans cevans at chyden.net No one ever says, "First shoot all the plumbers." Steve Foerster On 1 Dec 2010, at 5:45 PM, ??? wrote:
Hi, all,
a question regarding the cointegration relations (vectors) estimate
in the
Johansen test:
I have a data sample which is confirmed by the Johansen test as
cointegrated, however, if I take a subsample of the whole times
series, each
time add one data point and using the "ca.jo" function in R to
estimate the
cointegrating vector, i.e. to do a forward recursive test, and record
the
estimate beta (the first element of the vector is normalized to one,
beta is
the second element), strangely at some point, beta shows
discontinuity-a big
jump with sign change. This is really confusing to me as it seems
that the
Johansen procedure is not robust in that one additional data could cause
dramatical change in the estimate of beta. not sure if it is problem
of the
procedure or the ca.jo function, I think my data is fine (excluding
errors
and outliers). has anyone seen similar things as me?
Regards,
Paul C. Jin
[[alternative HTML version deleted]]
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
_______________________________________________ R-SIG-Finance at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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