Suppose that 11eb9b5b_3f38_5e41_bf3e_9dfb114d679e_SM2686_11 that 11eb9b5b_3f38_5e42_bf3e_610a8a3c8d3b_SM2686_11 follows the ARCH(1) model 11eb9b5b_3f38_8553_bf3e_e707270b289a_SM2686_11 and that the process for u t is stationary. Show that 11eb9b5b_3f38_d374_bf3e_e7f3a9b4e3ce_SM2686_11 . b. Extend the result in (a) to the ARCH( p ) model. c. Show that 11eb9b5b_3f38_fa85_bf3e_55917b6c6d2f_SM2686_11 for a stationary ARCH( p ) model. d. Extend the result in (a) to the GARCH(1,1) model. e. Show that 11eb9b5b_3f38_fa86_bf3e_7f8eeafff019_SM2686_11 for a stationary GARCH(1,1) model.

Introduction to Econometrics 3rd Edition by James Stock, James Stock

Edition 3ISBN: 978-9352863501

Edition 3ISBN: 978-9352863501

Exercise 15

Suppose that

that

follows the ARCH(1) model

and that the process for u t is stationary. Show that

.
b. Extend the result in (a) to the ARCH( p ) model.
c. Show that

for a stationary ARCH( p ) model.
d. Extend the result in (a) to the GARCH(1,1) model.
e. Show that

for a stationary GARCH(1,1) model.

Explanation

Verified

a) The ARCH(1) model for the variance of...