New answers tagged garch
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.
You find R code for seasonal ARIMA models again in the book mentioned (this chapter). Do you really need the GARCH errors?
You are right - GARCH model models volatility. They write: " The GARCH  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 ...
You first fit a ARIMA model to the returns data and then a GARCH model to the residuals.
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. ...
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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