[R-SIG-Finance] unstable cointegration vector estimates in Johansen test

Fri Dec 3 18:26:10 CET 2010

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 écrit :
> 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.
>
> Östermark, Ralf and Rune Höglund, 2000. Monte Carlo tests of 
> cointegration with structural breaks. Kybernetes 29 (9/10), 1284-1297.
>
> Östermark, Ralf and Rune Höglund, 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, 金陈琛 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]]
>>
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