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You can try: daily.fit=ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(35, 7), include.mean = T, arfima=F), fixed.pars=list(ar9=0,ar10=0,...,ar13=0,ar15=0,...,ar20=0,ar22=0,...,ar27=0,ar29=0,...,ar34=0,ma1=0,...,ma6=0)) from rugarch package.

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You find R code for seasonal ARIMA models again in the book mentioned (this chapter). Do you really need the GARCH errors?

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You are right - GARCH model models volatility. They write: " The GARCH [27] can be used to model changes in the variance of the errors as a function of time." What people often do is to fit an ARIMA model (that can be used to forecast a time series) and apply a GARCH model to the errors (which gives you a feeling for the forecast error). See Hyndman and ...

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You first fit a ARIMA model to the returns data and then a GARCH model to the residuals.

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alpha + beta < 1 is the stationary condition for GARCH. If alpha and beta are low that means volatility of the stock does not have clustering behaviors. I think you can have a look at ADF and PACF of Return^2 time series first. If the first order autocorrelation is very significant but alpha is not, then perhaps you can check on the parameter calibration. ...

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Heston gives an expression for the characteristic function, from which option prices can be computed. Therefore it can be calibrated (statically) on a set of vanilla option prices with different strikes and maturities. Hence this produces risk neutral parameters that can be used to price other more exotic products. However, it is a pain to estimate the ...

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