[R-SIG-Finance] Estimating co-integration factors of two time series

[Eric Zivot]

The "degree of cointegration" is not a well defined statistical concept. If
two series are cointegrated then there exists an error correction
representation for the bivariate system. You can estimate and analyze this
bivariate system and the properties of the system can tell you things like
(1) the speed of adjustment for each series in response to a deviation from
the long-run trend (2) the speed of mean reversion of the cointegrating
residual (3) whether a particular variable responds or not to the deviation
from the long run trend (ie which variables appears to be driving the
trend). You can also look at how well the error correction model fits (in
terms of R2) to get an idea of how useful it is for in-sample prediction.



-----Original Message-----
From: r-sig-finance-bounces at r-project.org
[mailto:r-sig-finance-bounces at r-project.org] On Behalf Of Pete Brecknock
Sent: Tuesday, October 25, 2011 10:11 AM
To: r-sig-finance at r-project.org
Subject: Re: [R-SIG-Finance] Estimating co-integration factors of two time
series


Russell Bowdrey wrote:
> 
> So, there appear to be many, many routines for testing for unit roots or
> hypothesis tests on co integration (ca.jo, ca.po etc)  - but I've yet to
> find a means of estimating the degree of co-integration between two time
> series.
> 
> IT could be that I'm going about this the wrong way (or looking for the
> wrong technique), so here is my problem (which I thought was common and
> had been solved...):
> 
> I want to measure the degree of co-movement between two assets or rates. 
> For example the yield on a bond and the corresponding risk-free rate.
> 
> Of course I could just look at Pearson/Spearman/Kendal correlation between
> the time series, but I believe that ignores time and so path dependence -
> which I think is important.  Hence thinking about cointegration.
> 
> Any thoughts?
> 
> 
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Perhaps Paul Teetor's example at
http://quanttrader.info/public/testForCoint.html maybe useful

HTH

Pete

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