1. (a) Why, in the recent finance literature, have researchers preferred GARCH(1,1) models to standard ARCH(p)? [10 marks] (b) Describe two extensions to the original GARCH model. What additional characteristics of financial data might they be able to capture? [10 marks] (c) Consider the following GARCH(1,1) model Yo = # + ur, W. ~N(0, of) (1) of = do + aut-1 + Boz_1 (2) where y, is a daily stock return series. What range of values are likely for the coefficients defined in equations (1) and (2)? [10 marks] (d) Suppose that a researcher wanted to test the null hypothesis that a, + 8 = 1 in equation (2). Explain how this might be achieved within the maximum likelihood framework. [10 marks]