  The block maxima method in extreme value theory consists of fitting an
extreme value distribution to a sample of block maxima extracted from a time
series. Traditionally, the maxima are taken over disjoint blocks of
observations. Alternatively, the blocks can be chosen to slide through the
observation period, yielding a larger number of overlapping blocks. Inference
based on sliding blocks is found to be more efficient than inference based on
disjoint blocks. The asymptotic variance of the maximum likelihood estimator of
the Fr\'{e}chet shape parameter is reduced by more than 18%. Interestingly, the
amount of the efficiency gain is the same whatever the serial dependence of the
underlying time series: as for disjoint blocks, the asymptotic distribution
depends on the serial dependence only through the sequence of scaling
constants. The findings are illustrated by simulation experiments and are
applied to the estimation of high return levels of the daily log-returns of the
Standard & Poor's 500 stock market index.
