No Evidence for GARCH in the Mean

Here's a first result using the excursion of DJIA daily volatility into the 300-400 points per day region. Does this market show any evidence of GARCH-in-the-Mean type behaviour? i.e. Does there seem to be a systematic bias to the drift of the market conditioned on the level of volatility. From the naive regression analysis, this hypothesis should clearly be rejected.

The more sophisticated approach of building a GARCH-M model directly, also fails.