A much more practical approach than calculating GARCH parameters on a calculator is to do it in R. Not only is there is available packages, retrieving financial data for experimenting is also a piece of cake as the facilities built-in offered convenient access to historical data.
To use GARCH in R the library must be installed first.
To test the library, data are imported using the tSeries package.
A plot of the log return.
Before running the GARCH model, a QQ plot is reviewed.
Finally, the GARCH model is created using the command below.
With trace=off a clean model can be printed after running the model.