I know that correlation is interdependence between two variables and cointegration is co-movement between two data sets BUT still I need more clarification and how to distinguish for a lay man with example.
Thanks.
Correlation gives a preview of the statistical relations between two or more variables. A high correlation coefficient amongst two variables implies that one variable has a strong economic/statistical relationship with another. As a researcher, one should be careful of accepting the verdict that there is 99% correlation amongst, say, two variables, this is perfect correlation which is very rare. Also on the other hand, if one gets 0% correlation coefficient, there is no statistical or economic relationships whatsoever. Co-integration on the other hand deals with long run equilibrium relationships between two or more variables, usually, a simple O.L.S model is run, residuals from such a model are obtained and tested for stationarity. If the residuals pass stationarity test, we could assert that there seems to be a long run relationship amongst the variables of interest. Hope this helps!
Correlation gives a preview of the statistical relations between two or more variables. A high correlation coefficient amongst two variables implies that one variable has a strong economic/statistical relationship with another. As a researcher, one should be careful of accepting the verdict that there is 99% correlation amongst, say, two variables, this is perfect correlation which is very rare. Also on the other hand, if one gets 0% correlation coefficient, there is no statistical or economic relationships whatsoever. Co-integration on the other hand deals with long run equilibrium relationships between two or more variables, usually, a simple O.L.S model is run, residuals from such a model are obtained and tested for stationarity. If the residuals pass stationarity test, we could assert that there seems to be a long run relationship amongst the variables of interest. Hope this helps!
If two series are driven by a common trend (cointegrated) you would expect the correlation you find in applied work to be quite high. However, even if two series are independent I(1) processes correlation between the two might still be fairly high though this relationship is spurious. Attached you will find a simple simulation with 1000 replications. When two series have a common trend simlple correlation is always positive and greater than 0.60 in all cases.
When you have two independent I(1) processes you do get correlations smaller than -0.6 or greater than 0.6 but only in 28 percent of the cases.
Of course the results might change depending on the spesific case you work with. Hope the attached Eviews Prg file and the text file with the results it gives would help.
Cheers,
Kenan Lopcu
You migth also want to check Enders, Applied Econometric Time Series, 4th Ed. Capter 6. Spesifically, Worksheet 6.1 and 6.2 migth be helpful.
Correlation is a measure of the (linear) relationship between stationary variables. For non-stationary variables correlation is spurious in the absence of cointegration. I would also recommend Ender's book (also recomymended by Kenan Lopcu) as a good introduction.
This is seemingly wrong:"A high correlation coefficient amongst two variables implies that one variable has a strong economic/statistical relationship with another." (Or I misunderstand it, just look at the many examples of high spurious correlations which are totally meaningless - Spurious correlations: Margarine linked to divorce? - BBC.com
www.bbc.com/news/magazine-27537142).
On a more scientific base, perhaps carefully look at the article by noble laureate Angus Deaton (http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2015/press.html):Journal of Economic Literature 48 (June 2010): 424–455
http:www.aeaweb.org/articles.php?doi=10.1257/jel.48.2.424
Instruments, Randomization, and
Learning about Development, e.g. p. 440: "One immediate charge
against such a procedure is data mining. A
sufficiently determined examination of any
trial will eventually reveal some subgroup
for which the treatment yielded a significant
effect of some sort, and there is no general
way of adjusting standard errors to protect
against the possibility. A classic example from
medicine comes from the ISIS-2 trial of the
use of aspirin after heart attacks (Richard
Peto, Rory Collins, and Richard Gray 1995).
A randomized trial established a beneficial
effect with a significance level of better than
10−6 , yet ex post analysis of the data showed
that there was no significant effect for trial
subjects whose astrological signs were Libra
or Gemini. In drug trials, the FDA rules
require that analytical plans be submitted
prior to trials and drugs cannot be approved
based on ex post data analysis."
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