Materi Analisis Deret Waktu Nonlinier

Universitas Brawijaya
Malang

MODEL GARCH,
IGARCH DAN GARCH-M
Eni Sumarminingsih, SSi, MM

GARCH
• Model GARCH (1,1)
Z Zˆ  a
t

t

a t  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