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  "body": "\n## Summary\n\nA moving-average model describes each value of a [[time series|EA3MF4VTEH]] as its mean plus a weighted sum of current and recent random shocks.\nWith $q$ past shocks the model is written MA($q$).\nIts autocorrelation vanishes beyond lag $q$, so it suits series whose memory is short.\nTogether with the autoregressive model it forms the ARMA family.\n\n## Explanations\n\n### L1 human\n\nImagine a pond where each raindrop makes ripples that last exactly two seconds.\nThe water level now is the sum of the effects of the drops of the last two seconds, and older drops no longer matter.\nIn the MA($1$) model $X_t = \\varepsilon_t + 0.5 \\varepsilon_{t-1}$, each shock acts fully today and half as strongly tomorrow, and then disappears.\nSo values two or more steps apart are uncorrelated.\n",
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