ECON 3350/7350 Volatility Models – I
Eric Eisenstat
The University of Queensland
Tutorial 7
Eric Eisenstat
(School of Economics)
ECON3350/7350 Week 7
1 / 2
Regressions and Autoregressions
Consider a regression for the mean of yt with ARCH(q) errors: yt =β1 +β2×2,t +…+βKxK,t +εt
ε = ν α + α ε2 + … + α ε2 tt01t−1 qt−q
whereνt ∼N(0,1),α(1)<1,α0 >0andE[εtνt−s]=0∀t,s Consider an autoregressive model, AR(1), of the mean of yt with
GARCH(1, 1) errors:
yt =a0 +a1yt−1 +εt |a1|<1
ε = ν α + α ε2 + β h
t t 0 1t−1 1t−1
α0, α1 and β1 to be non-negative, α1 + β1 < 1
Eric Eisenstat (School of Economics) ECON3350/7350 Week 7 2 / 2