# Regression - volatility vs return

I am attempting to estimate a linear model as: $$y = a +bX +e$$ I have a series of annual returns and I would like to estimate the effect of volatility on losses. My Null hypothesis is that volatility in period $t$ should have no linear relationship with losses in period $t+1$. So in actual fact, my model is: $$\min[0,y]t = a+bX_{t-1} +e$$ where $x$ is the standard deviation of $y$ in period $t-1$.

My questions are as follows:

1. What is the best way to test if my model is correctly specified?
2. Given that $X$ is rolled over in each period, should I be worried on the impact of serial correlations?
3. In the case of serial correlations, can this be better reduced by using higher lags of $X$?