Transcript GARCH

Universitas Brawijaya
Malang
MODEL GARCH,
IGARCH DAN GARCH-M
Eni Sumarminingsih, SSi, MM
GARCH
• Model GARCH (1,1)
Z  Zˆ  a
t
t
at   t  t
t
Model GARCH (m,s)
Identifikasi
Untuk identifikasi, gunakan ACF dan PACF
untuk sisaan kuadrat
• Pendugaan parameter
Sama dengan pada model ARCH, ganti
 Dengan model GARCH
• Peramalan Volatilitas GARCH(1,1)
Peramalan 1 langkah ke depan digunakan
Untuk peramalan banyak langkah ke depan,
gunakan
dan
Saat
, persamaannya menjadi
Karena
, maka
peramalan 2 langkah ke depan adalah
Secara umum peramalan l langkah ke
depan adalah
THE INTEGRATED GARCH
MODEL
An IGARCH(1, 1) model can be written as
THE GARCH-M MODEL
• In finance, the return of a security may
depend on its volatility
• To model such a phenomenon, one may
consider the GARCH-M model, where “M”
stands for GARCH in mean
• A simple GARCH(1, 1)-M model can be
written as
• where μ and c are constant
• The parameter c is called the risk premium
parameter
• A positive c indicates that the return is
positively related to its past volatility
• Other specifications of risk premium have
also been used in the literature, including
• For illustration, we consider a GARCH(1,
1)-M model for the monthly excess returns
of S&P 500 index from January 1926 to
December 1991.
• The fitted model is