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Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF)

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The instructor has "covered" Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), but I have not yet grasped a full understanding. Could you give me a cursory explanation now? I do know how to call up the ACF and PACF graphs but her explanation of how to use them and what they mean was not very clear.

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The solution examines autocorrelation functions and partial autocorrelation function.

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Autocorrelation Function (ACF)
The autocorrelation function of a stationary time series at lag k is defined as the correlation at lag k between and .
Partial Autocorrelation Function (PACF)
The partial autocorrelation function, like the autocorrelation function, conveys vital information regarding the dependence structure of a stationary process. The partial auto correlation at lag k may be regarded as the correlation between and, adjusted for the intervening observations. Thus the partial autocorrelation is the correlation of the two residuals obtained after regressing and on the intermediate observations .
Concept of ACF: The autocorrelation at lag k is the correlation between the values of the same variable and ___. In other words autocorrelation at lag k is determined by finding the correlation coefficient of the paired observations (Y1, Yk+1), (Y2, Yk+2), (Y3, Yk+3),... For example, autocorrelation at lag 1 is determined by computing the correlation coefficient of the observations (Y1, Y2), (Y2, Y3), (Y3, Y4),..., autocorrelation at lag 2 is determined by computing the correlation coefficient of the observations ...

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