Question: 17.3 Suppose that E(ut ut - 1, ut - 2, . . .) = 0 and ut follows the ARCH process, s2t = 1.0

17.3 Suppose that E(ut  ut - 1, ut - 2, . . .) = 0 and ut follows the ARCH process, s2t

= 1.0 + 0.5 u2t

- 1.

a. Let E(u2t

) = var(ut) be the unconditional variance of ut. Show that var(ut) = 2. (Hint: Use the law of iterated expectations, E(u2t

) = E3Eu2t

 ut - 1)4.)

b. Suppose that the distribution of ut conditional on lagged values of ut is N(0, s2t

). If ut - 1 = 0.2, what is Pr(-3 … ut … 3)? If ut - 1 = 2.0, what is Pr(-3 … ut … 3)?

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