Autocorrelation Clarification

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Could anyone help clarify a high level explanation of autocorrelation? I understand that it is a measure of correlation between a timeseries and a lagged version of the same series.

If we have take as an example the following series: 6, 2, 3, 8, 5, 2 Using acf() in R gives us -0.16 for lag 1

Why is this not the same as taking a pearson correlation coefficient against series 0, 6, 2, 3, 8, 5, nor 2, 3, 8, 5, 2, 0? Is the autocorrelation measure a completely different coefficient?

Have I also misunderstood how lag is applied?

Many thanks