Sains Malaysiana 47(9)(2018): 2195–2204

http://dx.doi.org/10.17576/jsm-2018-4709-30

 

Variance Targeting Estimator for GJR-GARCH under Model’s Misspecification

(Penganggar Sasaran Varians untuk GJR-GARCH di bawah Model Spesifikasi Ralat)

 

MUHAMMAD ASMU’I ABDUL RAHIM, SITI MERIAM ZAHARI^* & S. SARIFAH RADIAH SHARIFF

 

Centre for Statistical and Decision Science Studies, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 45450 UiTM Shah Alam, Selangor Darul Ehsan, Malaysia

 

Received: 21 November 2017/Accepted: 17 May 2018

 

ABSTRACT

 

The application of the Variance Targeting Estimator (VTE) is considered in GJR-GARCH(1,1) model, under three misspecification scenarios, which are, model misspecification, initial parameters misspecification and innovation distribution assumption misspecification. A simulation study has been performed to evaluate the performance of VTE compared to commonly used, which is the Quasi Maximum Likelihood Estimator (QMLE). The data has been simulated under GJR-GARCH(1,1) process with initial parameters ω = 0.1, α = 0.05, β = 0.85, γ = 0.1 and an innovation with a true normal distribution. Three misspecification innovation assumptions, which are normal distribution, Student-t distribution and the GED distribution have been used. Meanwhile, for the misspecified initial parameters, the first initial parameters have been setup as ω = 1, α = 0, β = 0 and γ = 0. Furthermore, the application of VTE as an estimator has also been evaluated under real data sets and three selected indices, which are the FTSE Bursa Malaysia Kuala Lumpur Index (FBMKLCI), the Singapore Straits Time Index (STI) and the Jakarta Composite Index (JCI). Based on the results, VTE has performed very well compared to QMLE under both simulation and the applications of real data sets, which can be considered as an alternative estimator when performing GARCH model, especially the GJR-GARCH.

 

Keywords: GJR-GARCH; QMLE; variance targeting; volatility

 

ABSTRAK

 

Penggunaan Penganggar Sasaran Varians (VTE) telah dipertimbangkan terhadap model GJR-GARCH (1,1) menggunakan tiga senario spesifikasi ralat, iaitu terhadap model, parameter awalan dan andaian taburan hingar. Kajian simulasi telah dilakukan untuk menilai prestasi VTE berbanding dengan Penganggar Kebolehjadian Kuasa Maksimum (QMLE). Data telah disimulasikan di bawah proses GJR-GARCH (1,1) dengan parameter awalan, ω = 0.1, α = 0.05, β = 0.85, γ = 0.1 dan hingar yang dianggap mempunyai taburan sebenar yang normal. Tiga andaian telah digunakan terhadap spesifikasi ralat bagi taburan hingar iaitu taburan normal, taburan t dan taburan GED. Sementara itu, spesifikasi ralat bagi parameter awalan telah ditetapkan sebagai ω = 1, α = 0, β = 0 dan γ = 0. Selain itu, penggunaan VTE sebagai penganggar juga telah dinilai menggunakan data sebenar iaitu Indeks FTSE Bursa Malaysia Kuala Lumpur (FBMKLCI), Indeks Masa Selat Singapura (STI) dan Indeks Komposit Jakarta (JCI). Berdasarkan keputusan analisis, VTE menunjukkan hasil anggaran yang lebih baik berbanding QMLE bagi kedua-dua kajian simulasi dan kajian berasaskan data sebenar. Oleh itu, VTE boleh digunakan sebagai penganggar alternatif bagi model GARCH, terutamanya GJR-GARCH.

 

Kata kunci: GJR-GARCH; QMLE; penganggar sasaran varians (VTE); volatility

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*Corresponding author; email: mariam@tmsk.uitm.edu.my