= Long-run variance of a stationary process
{title2=$\sigma_{\mathrm{LR}}^2=\sum_h\gamma(h)$}
With absolutely summable <autocovariance>, the asymptotic variance of the sample mean satisfies
$$
T\operatorname{Var}(\overline X_T)\longrightarrow\sum_{h\in\mathbb Z}\gamma(h)=2\pi f(0).
$$
The sum is signed, rather than a sum of absolute values. It can be zero: the first difference of <strong white noise> has telescoping partial sums. A <central limit theorem> needs further dependence assumptions.
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