2
$\begingroup$

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.

$\endgroup$
3
$\begingroup$

No. Your have overlapping observations. The first and the second observations have 89 seconds of overlap, they are clearly heavily correlated.

$\endgroup$
  • 1
    $\begingroup$ 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. $\endgroup$ – whuber May 13 '14 at 20:41
  • $\begingroup$ @whuber, I agree that lack of correlation doesn't imply lack of dependence, but not sure I understand the AR-1 example. $\endgroup$ – Aksakal May 13 '14 at 21:16
  • $\begingroup$ Thanks for the comments. What type of statistical analyses would you suggest for such kind of data? Is paired t-test ok, if I want to test the hypothesis if the means of the two samples are equal? Are there other methods that make sense in this scenario? $\endgroup$ – Frank D May 14 '14 at 15:56
  • $\begingroup$ One way to proceed is with HAC estimator, such as Newey-West. Basically, you run a usual regression, then adjust the coefficient variances with a special procedure. $\endgroup$ – Aksakal May 14 '14 at 15:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.