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In the paragraph before the one from which you gave the quotation is written such a thing: “…when u_i^2 is high, there is a tendency for u_(i+1)^2, u_(i+2)^2, … to be high; when u_i^2 is low, there is a tendency for u_(i+1)^2, u_(i+2)^2, … to be low.” This means that they (u_(i+1)^2,u_(i+1)^2, u_(i+2)^2,…) are correlated. Which by itself means that u_i^2 ...


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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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