A nonparametric block bootstrap series

for a simulated time series

is generated and the sample autocorrelations at lags 1, …, 10 for the

and

series are compared. The

series is simulated as an ARMA(1,1),

, where the

are independent normal random variables with mean 0 and variance 1. The theoretical autocorrelation for the ARMA(1,1) series is shown by the light gray lines and the sample autocorrelations of the

series by the orange lines. The blue points show the sample autocorrelations of the simulated bootstrap series. The block size parameter

may be fixed or in the stationary case it is randomly distributed with a mean of

from a truncated geometric distribution.