I know there are complex patterns in a series that cannot be detected by autocorrelation... but I cannot find what types of patterns these are. Can anyone provide an instance where the autocorrelation does not pick up on a pattern or provide a link to a site that provides examples of this?
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1$\begingroup$ Autocorrelation, being a function of just first and second moments of the multivariate distribution, has the same limitations as correlations in any bivariate distribution. The classical set of examples is given by Anscombe's quartet. $\endgroup$– whuber ♦Commented May 19, 2015 at 13:57
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$\begingroup$ What about for non random time series, where the autocorrelation plot is looking for a pattern in the response variable with the y-axis being the autocorrelation and the x-axis being the lag. $\endgroup$– DaveRowanCommented May 19, 2015 at 14:20
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$\begingroup$ The regular patterns will show up in autocorrelation plots. $\endgroup$– AksakalCommented May 19, 2015 at 14:30
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$\begingroup$ Randomness is irrelevant: the computation and interpretation of moments is the same regardless. The "one aspect" referred to in your Google Books reference specifically means the first and second order behavior. $\endgroup$– whuber ♦Commented May 19, 2015 at 15:22
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