See e.g. [Confidence interval estimation of the mean of stationary stochastic processes: A comparison of batch means and weighted batch means approach][1] and [Using standardized time series to estimate confidence intervals for the difference between two stationary stochastic processes][2]
and references therein. 


  [1]: https://www.researchgate.net/publication/236111526_Confidence_interval_estimation_of_the_mean_of_stationary_stochastic_processes_A_comparison_of_batch_means_and_weighted_batch_means_approach?enrichId=rgreq-3421a9c1ef72c04de8129f1dfaa86784-XXX&enrichSource=Y292ZXJQYWdlOzIzNjExMTUyNjtBUzoxMDMyODA0ODI5Nzk4NDNAMTQwMTYzNTM5NDIxNg%3D%3D&el=1_x_3&_esc=publicationCoverPdf
  [2]: https://www.jstor.org/stable/170544?seq=1