# Modeling independent variables that have an asymmetric impact on the dependent variable

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.

• Are you regressing the variable levels or returns ? – Ezy Jan 9 at 0:13
• I'm regressing the variable levels. – Ajk Jan 9 at 0:56
• If it at all helps, the independent variable(s) are different flavors of vol--close on close, intra-day, and implied vol. – Ajk Jan 9 at 2:42
• Have you tried regressing the changes of the dep against 2 terms being the positive changes of the indep and the negative changes of the indep ? – Ezy Jan 9 at 15:31
• @Ezy that’s an interesting suggestion. I have a similar issue at present. Thanks for the idea – uday Jan 11 at 4:17

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.