= Autoregressive conditional heteroscedasticity
{title2=$\sigma_t^2=\alpha_0+\sum_j\alpha_jX_{t-j}^2$}
= ARCH
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{synonym}
= ARCH process
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{synonym}
An ARCH model writes $X_t=\sigma_t\varepsilon_t$ with standardized independent driving noise and a <conditional variance> $\sigma_t^2=\alpha_0+\sum_{j=1}^p\alpha_jX_{t-j}^2$. Typically $\alpha_0>0$ and $\alpha_j\geq0$ ensure a positive conditional <variance>. It allows a changing conditional scale even when $X$ is a <stationary process>.
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