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Hey guys I'm trying to answer a question 'according to folklores, negative returns tend to cause more volatility than positive ones. Does this hold for the DJCA return series?'

I'm unsure how I can show if this is true or not, any help would be greatly appreciated thanks

You need to look at assymetric Garch models. Look in the user manual for "threshold Garch" aka GJR-Garch. Also, you should look at Exponential Garch.

I believe there is also a thread on "News Impact Curves" which is a graphical representation of assymetric volatility.