Autocorrelation and Spectrum Density
Fat32's answer is correct and shows a common pitfall.
The reason that you must do this is because recall that the output of the autocorrelation of a signal of length $N$ is $2N - 1$.
You were performing the FFT with the original sample size of $N = 1000$, effectively destroying necessary information to retrieve the autocorrelation of size $2N - 1 = 1999$.