How to account for filter delay

Hi all,

Its known that the delay for a FIR filter is (N-1)/2  where N is the
length of the filter and the filter is symmetric.

I am supposed to calculate the Mean Square Error between the input and
output of the filter. Since the length of the output will be greater than
the length of the input, I wanted to know how to relate the output of the
filter to the input of the filter.
i.e., if x(n) is the input
         y(n) is the ouput
         length of the filter is N
         length(x) = L
         length(y) = L+N-1
         therefore, length(y) > length(x)
But to calculate the mean square error the lengths of the 2 sequences has
to be equal. So how do I take into account the delay caused by the fir
filter.

Thanks.