For each of the asset groups you need a return series.  In the case of equities you may choose a stock market index. If you a finer grouping there may be an appropriate sectoral index ot otherwiseconstruct a portfolio of the required form. The other asset groups likee forex can be similarly calculateCd from an aggregate index or portfolio.

Art as a portfolio can be tracked using vaeiuos art investment fund returns. These are not dissimilar to property trusts or real estate investment trusts.You might be surp4ised to find the number of coll3ctible investment funds there are.  There was/is a barbie doll index.

Once you have the portfolios you can calculate common period returns.  These timeseries can be correlated using a parametric or nonparametric approach.

Thanks a lot. Could you suggest me a specific advaced statistical, econometrical methodology?

It could be rolling correlation, Evolutionary Co-spectral Analysis, Wavelet coherence, wavelet correlation based on MODWT decomposition, provided it's a high frequency data. 

• T-MDS (Threshold Minimum dominating Set) from Complex Networks Theory
• Multivariate GARCH models
• VARs - Impulse responses

If you think of ART instruments such as cat bonds they are known to be non correlated with market indexes, which is why they are attractive. A couple of surveys seem to validate this assertion.

I am currently doing a similar work based on Indian markets. Though it is unfinished, yet i am following the following process.

1. Time series for Stocks , Bonds, Gold and Art for a defined time period

2. Check the stochastic drift

3. Since all the movements are random in nature, so it will find out the possible connection between variables

Accordingly we can make a periodic conclusion

So, for better and more accurate modelling the time frame has to be fairly large.

Also, post this the fitment of both short duration and long duration models have to be checked for better fitment.

Regards

Bikram

 http://artemundiglob.com provides some potentially useful information on art investment fund. This next piece shows correlation with market in  figure 3;a nice zero beta portfolio.