I'm trying to regress a dependent variable on an independent variable that has an asymmetric impact. E.g., the dependent variable is much more responsive to an increase in the independent variable than it is to a similar decrease. Tried putting a dummy variable to indicate increases and decreases and then have that as an interaction term with the independent variable, but that did not seem to completely solve my problem. Any help would be much appreciated.
Okay, there are a couple of different problems based on your comments.
First, volatility measures are statistics and they are not data. You are using them as data. At one level this is okay in that you could have incorporated all the raw data to create them into your regression, but it is going to totally mess up all of your inferential statistics and all predictive measures.
The software that is used in the various forms of regression presumes you are inputting data only. From this, they estimate the sampling distribution of the statistics. Summary statistics used as data create completely incorrect math. The package assumes that you are calculating $f(x)$, when you are really calculating $f(x,g(y))$ or $f(g(y))$. Second, most volatility measures are non-linear. If you don't mind giving up the inferential value and predictive value and only want point response measures, you need to match the math of the underlying variables that make up those statistics to the new level.