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  "body": "\n## Summary\n\nAn autoregressive conditional heteroskedasticity (ARCH) model is a [[time series|EA3MF4VTEH]] model with a changing variance.\nThe [[conditional variance|0VGPX25NXQ]] of today's shock depends on the squares of past shocks.\nIt describes series whose volatility changes over time and comes in clusters, which is typical of financial returns.\nThe model was introduced by Robert Engle, and its extension GARCH also lets past conditional variances enter the equation.\nIt is a basic example of [[heteroscedasticity|D8VX6XQ3TT]] in time.\n\n## Explanations\n\n### L1 human\n\nStock prices move calmly for a while and then wildly for a while.\nAn ARCH model captures this: after a big move, the next move is likely to be big too, in either direction.\nThe size of the noise today is computed from how large the recent noises were.\nFor example, in an ARCH(1) model the variance today is $\\alpha_0 + \\alpha_1 \\varepsilon_{t-1}^2$, so a large surprise yesterday raises the uncertainty today.\n",
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