If data shows long-range temporal correlations, covariance is supposed to decay slowly with increasing temporal distance. The covariance should possibly approach zero? However I happen to have a dataset where the covariance turns negative when the temporal distance increases. Have I done something wrong?
Practically, I have 300 observations. I take the variance of the first 200. Then covariance between observations 1-200 and 2-201, then 1-200 and 3-202, and so on, until 1-200 and 201-300. When the temporal distance exceeds 50, the covariance turns negative. Temporal correlations do not vanish?
Problem solved. The data peaks in the middle of the time range. Correspondingly there is a positive covariance between arrays taken from the first half. Then there is a negative covariance between datasets taken from the beginning and from the end of the time series. Thank you for those who considered answering.
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