# Does nonparametric bootstrapping work on correlated data?

I have $m$ weakly stationary observations $X_1,X_2,\cdots,X_m$ from a Markov chain. I want to estimate the variance of the mean. My idea was to use nonparametric bootstrapping to make $n$ bootstrap samples from the $m$ observations and compute $n$ bootstrap means $\mu^*_i$. Then estimate the variance using $$\widehat{\mathrm{Var}(\overline X)} = \frac{1}{n-1}\sum_{i=1}^n ( \mu^*_i - \overline \mu^*)^2$$ Is it a problem that the observations are correlated, or is this fine?

• By "unparameterised bootstrap" do you mean nonparametric bootstrap or are you referring to something else? – Glen_b Jul 9 '17 at 13:58