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I am trying to find whether there is significant volatility transmission between two price series (t=1000). A literature review learned me that the GARCH BEKK model is suitable for this.

The SAS package can estimate it, see user guide However, I am getting strange results. Now I am in doubt about whether I am doing this the right way. I thought I should just make sure the series are stationary by first differencing them and afterwards, I can directly put them into the GARCH BEKK model by SAS.

Like this:

proc varmax data=price-series;
model series1 series2; 
garch q=1 p=1 form=bekk;
run;

Which steps am I overlooking?

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should be price returns, transforming your series as return=ln(Pt/Pt-1), in words, it means the natural logarithmic transformation of the ratio of price at time t to price at time t-1

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