Before prediction you should see which models fit better your data. First before choosing a GARCH model or a GARCH type model with leverage efect you shoud perform the Engle-Ng sign bias test to see if the asset that your are modelling is affected by it, if yes a simple GARCH model won't be a good model. After the estimation and given that all parameters are significant compere the information criteria; for example the Akaike, Bayes or Hannan-Quinn and see which model has the smallest one. With this you should select the model and then perform a prediction, and you can evaluate the performance of it with a back test. I have personally done this and usually an APARCH with generalize hyperbolic distribution is the best if the data present leverage erect.
UPDATE
Sure this is what I did with r
and the package rugarch
for the stock of EXITO a Colombian company:
1) fit a GARCH(1,1):
garch11Spec=ugarchspec(variance.model = list(model='sGARCH',garchOrder=c(1,1)),mean.model=list(armaOrder=c(0,0)))
garch11Fit=ugarchfit(garch11Spec,rtn) ## rtn is the date which is daily last price
2) Engle-Ng sign bias for leverage effect:
signbias(garch11Fit)
t-value prob sig
Sign Bias 0.19343098 0.8466364
Negative Sign Bias 0.15413313 0.8775166
Positive Sign Bias 0.02615509 0.9791356
Joint Effect 0.06291070 0.9958816
see that all p-values are higher than 0.1 son you don't reject the null hypothesis so there is no leverage effect
3) Look at the coefficients (the robust version) and there p-value, you will expect that all of theme to be statistically significant
garch11Fit@fit$robust.matcoef
Estimate Std. Error t value Pr(>|t|)
mu 3.735730e-05 1.237313e-04 0.3019229 7.627109e-01
omega 1.238605e-05 5.156212e-08 240.2160962 0.000000e+00
alpha1 2.517465e-01 5.271207e-02 4.7758795 1.789235e-06
beta1 5.822453e-01 3.733553e-02 15.5949369 0.000000e+00
4) Information criteria:
infocriteria(garch11Fit)
Akaike -6.941621
Bayes -6.932700
Shibata -6.941626
Hannan-Quinn -6.938391
you want the smallest value possible
Here are the 4 steps together for the aparch:
signbias(aparchFit)
t-value prob sig
Sign Bias 0.17982812 0.8573014
Negative Sign Bias 0.05186043 0.9586438
Positive Sign Bias 0.57709943 0.5639217
Joint Effect 0.35736070 0.9489028
aparchFit@fit$robust.matcoef
Estimate Std. Error t value Pr(>|t|)
mu 0.0000186132 0.0001385818 0.1343120 8.931558e-01
omega 0.0019649457 0.0004959927 3.9616428 7.443584e-05
alpha1 0.2521930795 0.0433561290 5.8167804 5.999189e-09
beta1 0.5734338681 0.0809929461 7.0800470 1.441069e-12
**gamma1 0.0482664316 0.0886992553 0.5441583 5.863326e-01**
delta 1.0000000000 NA NA NA
you can see, gamma1 which is the leverage effect parameter is not significant, p-value = 0.58 as expected, so not a good model
infocriteria(aparchFit)
Akaike -6.942806
Bayes -6.931655
Shibata -6.942813
Hannan-Quinn -6.938769
if you compera the criteria with the GARCH(1,1) you can se that the Bayes and the Hannan-Quinn are smaller in the first model, the other 2 smaller for the aparch but YOU KNOW that the aparch isn't the right model because there is NO leverage effect, can't just trust the information criteria you have to understand the models to select one. With this stock is easy because it has no leverage effect so you have to stick with a GARCH(1,1) if you get leverage effect should perform this with the different model that you want to use to find the best.
If after doing this with the differnt models you don't have a clear winner do a back test on the prediction and compere the RMSE, MSE or MAE and also do a VaR backtest as the other comment says