Let's discuss academic research on mean-reverting trading strategies...

Random.Capital · Sep 17, 2009

In practical terms, cointegration is just correlation with error bars. Or if you prefer, correlation is the spread between two instruments being (relatively) fixed, while with cointegration the spread between the two instruments is mean-reverting.

Same family, different cousin - at root, it's all the same assumption.

Equalizer · Sep 17, 2009

Quote from intradaybill:

It is true that correlation does not imply cointegration. I think we can agree to that.

Cointegration implies correlation when the residuals are stationary. When the residuals are normal, there is longer term correlation.

In the paper you posted there is a basic error in that if the residuals are random the two series are not cointegrated and you cannot know that from a limited sample.

I thus insist, cointegration implies correlation, but not vice versa.

We are a little off-topic here, but I believe you are still wrong.

Please refer to Dr West's excellent paper:

http://www.finmod.co.za/Westprime.pdf
Graeme West. Interest rate derivatives in the South African Market based on the prime rate. Journal for Studies in Economics and Econometrics, 2008, 32(1)

In particular, refer to section 3.

You can put together an example showing high cointegration but very low correlation. Refer to the gummy-stuff link I gave earlier.

dtrader98 · Sep 17, 2009

Quote from intradaybill:

Cointegration implies correlation when the residuals are stationary.

You got that backwards. It's correlation implies co-integration when residuals are stationary, not the other way around.

Nor is (as the prior poster or two stated) the spread between two instruments, a co-integrated and mean reversing process.
It is a particular linear combination of two instruments (one being weighted relative to the other) that qualifies as a candidate for a co-integrated series.

Equalizer · Sep 17, 2009

Quote from dtrader98:

You got that backwards. It's correlation implies co-integration when residuals are stationary, not the other way around.

Nor is (as the prior poster or two stated) the spread between two instruments, a co-integrated and mean reversing process.
It is a particular linear combination of two instruments (one being weighted relative to the other) that qualifies as a candidate for a co-integrated series.

Correct. These are not difficult concepts, but I believe people should do some Excel work and visualise the results for themselves.

warrenmurdoch · Sep 17, 2009

Thank you for posting the paper. The following quote summarizes my understanding of correlation and cointegration.

"High correlation does not imply high cointegration, or vice virsa. In fact cointegrated series can have correlations that are quite low at times. For example, an index-tracking portfolio
should be cointegrated with the index."

This pdf http://www.uh.edu/~bsorense/coint.pdf is a good summary of cointegration from an econometrics course.

Carol Alexander's book "Market Models" pp 349-350 discusses correlation and cointegration.

dtrader98 · Sep 17, 2009

Quote from Equalizer:

Correct. These are not difficult concepts, but I believe people should do some Excel work and visualise the results for themselves.

Amen.
The best advice anyone could ever heed regarding these concepts.

Regarding the common misconception about correlation being a necessity for co-integraton, let me quote from Carol Alexander, whom another poster has just referenced (she is chair of risk mgmt University of Reading (ICMA)).

"Cointegration measures long-run co-movements in prices, which may occur even through periods when static correlations appear low."

intradaybill · Sep 17, 2009

Quote from warrenmurdoch:

In fact cointegrated series can have correlations that are quite low at times.

So what? Neither cointegration, nor correlation are absolute properies. At times, highly correlated series can be low correlated. The same holds for cointegration.

Stupidity and low grades are highly correlated. At times, stupid people can get high grades because of chance. So what?

intradaybill · Sep 17, 2009

Quote from dtrader98:

"Cointegration measures long-run co-movements in prices, which may occur even through periods when static correlations appear low."

This is a meaningless statement, mathematically speaking. When you evaluate certain mathematical properties you must consider the same horizon. If you take a snapshot, a curve may look like a line. Can you say that curves at times look lke lines in general?

Random.Capital · Sep 17, 2009

Quote from dtrader98:

Nor is (as the prior poster or two stated) the spread between two instruments, a co-integrated and mean reversing process.

That isn't even close to what the "prior poster" said.

zzt · Sep 17, 2009

Quote from intradaybill:

It is true that correlation does not imply cointegration. I think we can agree to that.

Cointegration implies correlation when the residuals are stationary. When the residuals are normal, there is longer term correlation.

In the paper you posted there is a basic error in that if the residuals are random the two series are not cointegrated and you cannot know that from a limited sample.

I thus insist, cointegration implies correlation, but not vice versa.

I have to jump in here...dude you have it wrong. Cointegration does not imply correlation, although, correlation and cointegration often do co-exist. ( Is that what you mean when you say 'implies' ?)

Aditionally, there seems to be an assumption in previous posts that stat arb strategies have been slammed by the recent crisis related volatility. The opposite is true...any stat arbs i know have been making boatloads