Materi Analisis Deret Waktu Nonlinier

Universitas Brawijaya

Malang

MODEL GARCH,

IGARCH DAN GARCH-M

GARCH

• _{Model GARCH (1,1)}

Identifikasi

• _{Pendugaan parameter}

Sama dengan pada model ARCH, ganti

• _{Peramalan Volatilitas GARCH(1,1)}

Peramalan 1 langkah ke depan digunakan

Saat , persamaannya menjadi

Karena , maka

THE INTEGRATED GARCH

MODEL

THE GARCH-M MODEL

• _{In finance, the return of a security may}

depend on its volatility

• _{To model such a phenomenon, one may}

• _{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}

• _{A positive c indicates that the return is}

positively related to its past volatility

• _{Other specifications of risk premium have}

• _{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.