Here there are another approaches to the topic

A set of novel correlation tests for nonlinear system variables- ?epsrcham.org.uk [PDF] 
 http://www.epsrcham.org.uk/Papers_files/2007%20Vol%2038%20No%201%20IJSS.pdf
LF Zhang, QM Zhu, A Longden - International Journal of Systems Science, 2007 - informaworld.com


A nonlinear correlation measure for multivariable data set
Q Wang, Y Shen, JQ Zhang - Physica D: Nonlinear Phenomena, 2005 - Elsevier


In R Package tseriesChaos has some measures for nonlinearity in a time series from
http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/TiseanHTML.html

" All these nonlinear correlation tests have their individual drawbacks." Zhang et al

 
From: Mark Breman 
Sent: Friday, June 05, 2009 4:07 PM
To: r-sig-finance@stat.math.ethz.ch 
Subject: Re: [R-SIG-Finance] determine non-linear correlation


Here is the thesis I was talking about (see attached pdf file)


I am working on an illustration (example) of the problem I'm trying to solve. I will post it to this group this weekend...


Regards,


-Mark- 





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From: KAUSHIK BHATTACHARJEE <kabonline07@yahoo.com>

Sent: Friday, June 5, 2009 1:18:55 PM
Subject: Re: [R-SIG-Finance] determine non-linear correlation


correlation by definition is a linear measure of assocation. So what is the presice definition of non-linear correlation?
can you give the thesis......I am curious to know....

Kaushik Bhattacharjee




--------------------------------------------------------------------------------

To: r-sig-finance@stat.math.ethz.ch
Sent: Thursday, June 4, 2009 12:45:17 AM
Subject: [R-SIG-Finance] determine non-linear correlation

I would like to know if two financial time-series are nonlinear correlated, and if so, what that correlation function is.
Is there an easy way to do this with R?

I have read a thesis about the "high order correlation coefficient to solve the nonlinear correlation problem" but I'm not able to translate this into a solution for my problem. All these statistics are very interesting but also challenging for me...  

Kind regards,

-Mark-
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