Effective sample size of a stationary sample ($T_{\mathrm{eff}}=T\gamma (0)/{\sigma }_{\mathrm{LR}}^2$)

When the long-run variance of a stationary process is positive, matching the variance of its average to an average of independent observations gives $T_{\mathrm{eff}}\simeq T\gamma (0)/{\sum }_h\gamma (h)$. Positive aggregate correlation reduces this size; negative aggregate correlation can increase it beyond the observation count. This extends the variance interpretation of effective sample size of a Markov chain.