Econometrics - Assessment Questions

Question 1

Question 1 Let rt denotes the return of a financial asset and σt denotes the standard deviation of returns at time t, 

1. Write down an AR (1)-ARCH (q) model with q=4.
2. Write down an AR (1)-GARCH (q, p) model with q=1 and p=2
3. Derive the unconditional means of AR (1)-ARCH (4) model and AR(1)- GARCH(1,2) model in (a) and (b) (Show steps and specify the conditions if required).
4. Derive the unconditional variances of AR(1)-ARCH(4) model and AR(1)- GARCH(1,2) model in (a) and (b) (Show steps and specify the conditions if required).
5. Discuss and compare an ARCH(1) model and a GARCH(1,1) model.

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