In this tutorial, an Automated Selection for ARCH-GARCH modeling procedure is applied for the Unemployment Rate in U.S. monthly data starting from 1980 to 2019 December. The purpose is to find the best model based on 4 different criteria, namely AIC, BIC, Test RMSE, Test MAPE. This way, 4 different model is suggested for the decision maker and s/he can choose among them having the lowest criteria for his/her own purpose.
Note that there are various ways of selecting the right order/model when it comes to ARCH-GARCH modeling since there is no exact 'right' way of doing it. That's why, the researcher should not directly trust the outputs. Hopefully, this tutorial will help him/her to give a reasonable path for his/her own selection processes.
While creating this model selection tutorial, mainly the article "A GARCH Tutorial with R" (Perlin et al,2021) inspired.
Perlin, Marcelo & Mastella, Mauro & Vancin, Daniel & Ramos, Henrique. (2021). A GARCH Tutorial with R. Revista de Administração Contemporânea. 25. 10.1590/1982-7849rac2021200088.
U.S. Bureau of Labor Statistics, Unemployment Rate [UNRATE], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/UNRATE, November 19, 2020.