Materi Analisis Deret Waktu Nonlinier

THE EXPONENTIAL GARCH
MODEL

THE EXPONENTIAL GARCH MODEL
• To allow for asymmetric effects between
positive and negative asset returns, he
considers the weighted innovation
• where θ and γ are real constants
• Both t and | t | − E(| t |) are zero-mean iid
sequences with continuous distributions

• Therefore E[g(t )] = 0
• The asymmetry of g(t ) can easily be seen by
rewriting it as

• An EGARCH(m, s) model can be written as

• where α0 is a constant
• B is the back-shift (or lag) operator such that
Bg(t ) =g(t−1)

• The use of g( t ) enables the model to respond
asymmetrically to positive and negative lagged
values of at

• To better understand the EGARCH model, let
us consider the simple model with order (1, 0)

• Specifically, we have

Example
• We consider the monthly log returns of IBM
stock from January 1926 to December 1997
for 864 observations.
• An AR(1)-EGARCH(1, 0) model is entertained
and the fitted model is

• For the 2-step ahead forecast