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Few comments on your questions: 1) Yes, Arch and Garch are suitable for equities volatility, please see: http://onlinelibrary.wiley.com/doi/10.1002/jae.800/pdf 2) No. These are models of volatility. To model interest rates use CIR, Vasicek or similar. 3) and 4) Check paper above.

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My 2 Zimbabwe cents: A few years ago developing new ARCH like models became almost a fad and large numbers of them were published without a clear justification in my humble opinion. However there is an important distinction I do think. Some markets are symmetric, while others (such as Stock Indexes) show a Leverage Effect where the volatility rises when ...

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You won't find a systematic approach, that would require the models to be arranged in some system, whereas generally each is an adjustment of GARCH. The best you can do is to know the usage cases of as many as possible and then use your own judgement as to which model is appropriate.

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Just a quick fix. Looking at the wikipedia entry of EGARCH: $g(\zeta_t)$ (the unit-scale random variable) seems correct - as you say.

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This are some comments to your problem. It appears that your are not sending appropriate series to the function. Try maegarch14<-(abs(garchf14$meanForecast-brentlogtest1[1:126])) and maeegarch14<-(abs(fitted(egarchf14)-brentlogtest1[1:126])). You need to pass at least vector series to that function. Are you sure h is 126? your result said 253! For ... 0 Garch models are not good to predict "many" periods ahead, but for "very short" times. If you want to predict 2 months from here, maybe you should be working with monthly data. I did a similar exercise with some indexes (symb=c("^BVSP","^MERV","^DJA","^N225")) using daily returns from="1991/01/01", look the incredible predictions. 1 So you are asking whether the function Box.test requires standardized or raw residuals as input? I do not know this function but as you mention that the results change based on your input it should be such that the function requires standardized values. In case a standardization is implemented directly the output should not differ because you either plug-in ... 0 This should follow from the properties of the forecast - for example the GARCH(1,1) forecast for$h$steps is computing the conditional expectation of$\sigma^2_{t+h}$based on the information set-up in$t$. This can be computed recursively by$\$ V(\varepsilon_{t+h}|F_t)=\omega+\alpha\varepsilon_{t+h-1|F_t}+\beta\sigma^2_{t+h-1|F_t}\\ ...

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