Motivated by Efron (1992, Journal of the Royal Statistical
Society, Series B 54, 83–111), this paper proposes
a version of the moving block jackknife as a method of estimating
standard errors of block-bootstrap estimators under dependence.
As in the case of independent and identically distributed (i.i.d.)
observations, the proposed method merely regroups the values
of a statistic from different bootstrap replicates to produce
an estimate of its standard error. Consistency of the resulting
jackknife standard error estimator is proved for block-bootstrap
estimators of the bias and the variance of a large class of
statistics. Consistency of Efron's method is also established
in similar problems for i.i.d. data.