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  "body": "\n## Summary\n\nAn autoregressive model describes each value of a [[time series|EA3MF4VTEH]] as a linear combination of a few past values plus a random shock.\nThe number of past values used is the order $p$, and the model is written AR($p$).\nIt is one of the simplest and most used models for dependent data, and a building block of ARMA and ARIMA models.\n\n## Explanations\n\n### L1 human\n\nThe model says that the present is a weighted echo of the recent past plus something new and unpredictable.\nIn the AR($1$) model $X_t = 0.8 X_{t-1} + \\varepsilon_t$, each value keeps $80\\%$ of the previous one and adds fresh noise.\nA shock therefore fades away slowly, by a factor $0.8$ each step.\nIf the weight were $1$, shocks would never fade, and the series would wander like a random walk.\n",
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