# Detecting stochastic volatility

I have a time series extracted from a financial time series (so my series of prices is described by an arithmetic model $X(t)+Y(t)+Z(t)$, my series is $Z(t)$). I'm trying to model $Z(t)$ by a Levy process. However, it might be the case that $Z(t)=\int_0^t \omega_{s-} dV_s$, where $\omega_{t}$ is a stochastic volatility and $V(t)$ - a Levy subordinator.
We can see that:

• My fit seems to be reasonable, $Z(t)$ has slightly fatter tails than the model.
• Increments of $Z(t)$ are uncorrelated.
• Squared increments of $Z(t)$ are slightly correlated.

My question: How can I "detect" stochastic volatility? I tried to look at ACF functions of the increments of $Z(t)$ (and squared increments), but I'm not sure what it would tell me. I'm looking for easy tests that could give me some intuition, not a definite answer.