C45. ACF and PACF

Topic: Dependence along a series · more questions on this topic
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What do the autocorrelation function (ACF) and partial autocorrelation function (PACF) measure?

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Definitions/notation. For a weakly stationary process with positive variance, the ACF at lag k is \rho(k)=\operatorname{Corr}(X_t,X_{t-k})=\gamma(k)/\gamma(0), where \gamma(k) is the autocovariance. The PACF is the correlation between the two endpoints’ residuals after their linear projections on the intervening observations X_{t-1},\ldots,X_{t-k+1} (no intervening adjustment at lag one).