Variance targeting estimator for GJR-GARCH under model’s misspecification

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.