This is a work for replicate
> set.seed(1)
> Series <- replicate(100, timeseriesmodel(250,1,0,1.2) ) # repeating 100 times `timeseriesmodel`
> dim(Series) # each result is store column-wise
[1] 250 100
> cor(Series[249,], Series[250,] ) # here's the correlation between element 249 and 250
[1] 0.9975532