Resampling methods are proposed to estimate the distributions of sums of m-
dependent possibly differently distributed real-valued random variables. Th
e random variables are allowed to have varying mean values. A non-parametri
c resampling method based on the moving blocks bootstrap is proposed for th
e case in which the mean values are smoothly varying or "asymptotically equ
al". The idea Is to resample blocks in pairs, It is also confirmed that a "
circular" block resampling scheme can be used in the case where the mean va
lues are "asymptotically equal". A central limit resampling theorem for eac
h of the two cases is proved. The resampling methods have a potential appli
cation to time series analysis, to distinguish between two different foreca
sting models. This is illustrated with an example using Swedish export pric
es of coated paper products.