When the random variables $X_1,...,X_n$ are i.i.d., then the sample variance $S^2=\frac{1}{n-1}\sum_{i=1}^n (X_i - \overline{X})^2$
has the variance
$\frac{\mu_4}{n} - \frac{ \sigma^4(n-3)}{n(n-1)}$
where $\mu_4$ is the fourth central moment of $X_1$ and $\sigma^2$
is the variance.
What is the sample variance if the variables $X_1,...,X_n$ are dependent (e.g. ARMA(p, q)-process)? Are there some results?