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GARCH models are essentially white noise models with some time dependency. The reason GARCH models are used is because they have a lot of nice properties. The main being that the Conditional Volatility is time-dependent. This means that volatility can cluster. It's true that conditional vol will regress towards "normality" as a random walk process with ...


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You can see fairly quickly that an exact answer to this question is not going to be feasible because your functional transformation is to take the square root of $\sigma_t^2$, and the square root function has a countably infinite number of derivatives. This implies that a Taylor expansion is going to leave us with a countably infinite number of terms, most ...


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"conditional volatilities from GARCH models are not stochastic since at time $t$ the volatility is completely pre-determined (deterministic) given previous values"-https://en.wikipedia.org/wiki/Stochastic_volatility $\sigma_t$ is still a random variable in the sense that it has an unconditional distribution. However, this unconditional distribution is not ...



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