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  "body": "\n## Summary\n\nThe partial autocorrelation function of a weakly stationary process gives, for each lag $h$, the correlation between $X_{t+h}$ and $X_t$.\nIt first removes the linear effect of the values in between.\nIt complements the [[autocorrelation function|YCZHYY8VE5]].\nFor an autoregressive model of order $p$ it vanishes beyond lag $p$.\nThis makes it the main tool for choosing the order of such a model.\n\n## Explanations\n\n### L1 human\n\nToday's value may be correlated with the value two days ago only because both are linked to yesterday's value.\nThe partial autocorrelation at lag $2$ asks what correlation is left once yesterday's value has been taken into account.\nIn a process where each value depends only on the previous one plus fresh noise, nothing is left: the partial autocorrelation at lag $2$ is $0$.\nThe ordinary autocorrelation at lag $2$ of the same process is not $0$, because the influence passes through the middle day.\n",
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