Measuring dependence in data series

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FatTail
Posts: 20
Joined: Sun Nov 16, 2008 10:07 am

Measuring dependence in data series

Postby FatTail » Thu Nov 20, 2008 10:45 pm

Dependence in data series can be of (a)dependence in the returns -first order (b) dependence in time varing volatility -second order.

I have data that i think may have both sorts of dependence - but am interested in both types. I am intuitely attracted to measures of dependence that use a measure of the data in its original ordered format and comparing this to the running the same measure against the same data but the data is scrambled, so the difference between the two measures is a test of whether the ordering of the data was really important.

I have looked around but not sure what are the standard tests that work in this way. Any thoughts?

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Measuring dependence in data series

Postby coalexander » Fri Nov 21, 2008 9:11 am

Yes, good idea to use 'scrambled' data as a benchmark. I remember doing this in one of my papers on cointegration with Anca Dimitiru (can't remember which one it was now - so long ago - or maybe we never published it). We scrambled up the returns and reconstructed price series, then tested again for cointegration. This is really a test of the power of a cointegration test to detect no cointegration. With some tests (eg ADF) and in some simulations, we got a test result saying cointegration, when there could not be.

The standard dependence tests you talk about can be done using the usual "Portmanteau" form, i.e. Lagrange Multiplier tests of the form TR_squared, where R-squared is something. For instance, for autocorrelation in returns, use the sum of the squares of the autocorrelations up to pth order for R_squared, then TR_squared is a chi-squared with p degrees of freedom. Can do the same for autocorrelation in squared returns, just replace return with squared return, which the standard GARCH test for volatility clustering. There are also asymmetric volatilty clustering LM tests, which I think I described in Market Models.

In each case, do the test on the data you have, then again on scambled data, to give you an idea of the power of the test.

Hope this helps, Carol


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