# Are samples from sliding windows independent samples?

Are samples from sliding windows independent samples? E.g. if I have window size of 90 seconds counting the number of cars on a street and I output the average within the window every second for 30 seconds, do I have 30 independent samples or not?

I'd say yes, as it looks (to me) like sampling with (partial?) replacement. But I'm not sure. I'm asking, because I thought if the samples were independent and I collected n>30, the central limit theorem could be used for further calculations.

• It might be of interest to note that when the window size is odd, it is possible (although, I admit, unusual) for two overlapping windows to be uncorrelated. For instance, with a window of size $89$ and an AR-1 series with serial correlation around $-0.985737,$ successive averages will be uncorrelated (but still highly dependent). This indicates that it would be better not to substitute lack of correlation for independence in reasoning about this question. – whuber May 13 '14 at 20:41