# Squared and Absolute Returns

I've always wondered why do one use squared or absolute returns to determine if volatility modeling is required for the return series? We understand that there are various tests for its autocorrelation and conditional heteroskedasticity. However, I don't quite grasp the concept behind it. Can anyone kindly explain what's the statistical intuition behind using squared/abs returns to determine if vol representation is needed? Thank you.

Also, often we can assume the average of short-term returns in the long run to be zero, the historic volatility is equal to $\hat{\sigma_T^2}=\frac{\sum_{i=1}^T{r_i^2}}{T-1}$. Sp to study the volatility process we therefore study the squared return process, which is a good proxy.