I checked the operations performed by Matlab and found that the built-in function autocorr() calculates the same unweighted function that the OP originally described (except that the mean value of the data is properly subtracted). This is fine for short lags but reduces the weight of peaks associated with large lags. From the autocorr help message "the form adopted here follows that of Box, Jenkins, and Reinsel ... Time Series Analysis: Forecasting and Control. 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 1994". I've attached a sample plot obtained by using the following Matlab script:
m=csvread('test.txt');
ACF=autocorr(m(:,2),969);
plot(ACF);
One can see how the peaks diminish as the lag increases, which I consider to be misleading. The Fourier transform of this particular autocorrelation function will not be the same as the power spectrum plot of the zero-filled FFT that I posted earlier.
