Given S&P500 returns for the past 20 years I fitted an ARMA(1,1)-GARCH(1,1) model using the rugarch package, so using ugarchspec() and the ugarchfit(), with different innovations distributions, i.e. norm, std, ged. My task would be to evaluate and compare the forecasting performance of the different models but I have problem to figure out how to do it. I then used the ugarchforecast as:
spec <- ugarchspec(variance.model = list("sGARCH", garch0rder = c(1,1), submodel = NULL, external.regressors = NULL, variance.targeting = F), mean.model = list(arma0rder = c(1,1), include.mean = T, archm = F, archpow=1, arfima = F, external.regressors = NULL, archex = FALSE), distribution.model = "norm", fixed.pars = list(ar1 = 0.6170, ma1 = -0.6824, mu = 2e-04)) garch <- ugarchfit(spec, ret, out.sample = 100, solver = "solnp", fit.control = list(stationarity = 1, fixed.se = 0, rec.init = "all")) fore <- ugarchforecast(garch, n.ahead = 100, n.roll = 100)
Is that procedure correct? what should I do now to evaluate the forecast performance by comparing MSE, RMSE, MAE?