Suppose that 11eb817c_7809_fc4a_84e6_65ed9e6b5eab_SM2685_11 that 11eb817c_7809_fc4b_84e6_53a44fe82670_SM2685_11 follows the ARCH(1) model 11eb817c_7809_fc4c_84e6_23ecd44e5fb5_SM2685_11 and that the process for u t is stationary. Show that 11eb817c_7809_fc4d_84e6_8b58f92207f9_SM2685_11 . b. Extend the result in (a) to the ARCH( p ) model. c. Show that 11eb817c_7809_fc4e_84e6_1f46fa00231e_SM2685_11 for a stationary ARCH( p ) model. d. Extend the result in (a) to the GARCH(1,1) model. e. Show that 11eb817c_7809_fc4f_84e6_6dbcd18f14db_SM2685_11 for a stationary GARCH(1,1) model.

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

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...