Question: You are working in a financial institution and your boss proposes to upgrade the financial risk-management methodology the company uses. In particular, to model the FTSE-100 index your boss suggests estimation using an ARCH(1) process. You disagree and wish to convince your boss that a GARCH(1,1) process is better.
(a) Explain, intuitively first, why a GARCH(1,1) process will fit the returns of FTSE-100 better than an ARCH(1) process.
(b) Prove your point with the use of mathematics.
(c) Estimate both models and try to analyse them in such a way that you can convince your boss about the preferability of the model you are proposing. Check the conditional standard deviation and conditional variance series as well.