Rule of Thumb for minimum length of time series for AR(1) estimation

Question

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data.

More precisely I want to take non overlapping windows of length 1,2,3....n and calculate the auto correlations of these sub-sets. So for n equal to 2 I take every second observation similarly for n=3 I take every third observation and so on.

Just wondered roughly what the maximum value of n I can realistically work with? Even with n=10 I'm down to 35 observations.

Kind Regards

Baz

Answer 1

Strictly speaking, it depends on the signal/noise ratio in your dataset. The smaller the variance of the white noise component, the fewer observations one needs.

Note also that all you need to estimate ACF for AR(1) is the autoregression coefficient, $\phi$, because the correlation between points $h$ time steps apart is equal to $\phi^h$. That is, if you assume AR(1) for the original process you don't need to do any subsetting to estimate autocorrelations.