I have $m$ weakly stationary observations $X_1,X_2,\cdots,X_m$. I don't know anything else about the observations. I want to estimate the variance of the sample mean. At first, my idea was to use nonparametric bootstrapping to do this. But I learnt that this method doesn't work for correlated data.

What are the most easy, standard ways of doing this to get reliable estimates?

  • $\begingroup$ If the observations are a time series with equal time intervals, why don't you take the differences between successive observations, bootstrap off those, reconstruct potential observations from the bootstrapped differences and thus sample means, and then take the variance of those? $\endgroup$ – Henry Jul 11 '17 at 0:31

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