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@jemoka / Jemoka Knowledge Base / wiki/concepts/garch.md
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--- title: "GARCH" type: concept related: [Heteroskedastic, Garch] source: https://www.jemoka.com/posts/kbhgarch/ confidence: high status: active --- The GARCH model is a model for the heteroskedastic variations where the changes in variance is assumed to be auto correlated: that, though the variance changes, it changes in a predictable manner. It is especially useful to GARCH 1,1 Conditional mean: \begin{equation} y_{t} = x’_{t} \theta + \epsilon_{t} \end{equation} Then, the epsilon parameter: \begin{equation} \epsilon_{t} = \sigma_{t}z_{t} \end{equation} where: \begin{equation} z_{t} \sim \mathcal{N}(0,1) \end{equation} and: conditional variance \begin{equation} {\sigma_{t}}^{2} = \omega + \lambda {\sigma_{t-1}}^{2} + \beta {\sigma_{t-1}}^{2} \end{equation} Finally, with initial conditions: \begin{equation} w>0; \alpha >0; \beta >0 \end{equation}