Confidence Intervals for strongly mixing stochastic processes

Question

I have $s(t)$, a stationary stochastic process that we know is strongly mixing - and I also know that samples from $s(t)$ are definitely correlated over time. I want to estimate the mean of $s(t)$, $\mathbb{E}[s(t)]$. Since strong mixing implies ergodicity, I can simply calculate sample means to find $\mathbb{E}[s(t)]$.

Does anyone know how I can go about estimating empirical variance so I can get confidence intervals for the estimated mean?

If $s(t)$ was Markovian, for example, I could use the Strong Markov Property to find empirical variance, but I have no clue how to do this for my general, non-Markovian $s(t)$.

Answer 1

See e.g. Confidence interval estimation of the mean of stationary stochastic processes: A comparison of batch means and weighted batch means approach and Using standardized time series to estimate confidence intervals for the difference between two stationary stochastic processes and references therein.