A Class of Non-Linear AGARCH(1,1) Model in Modeling Volatility of Returns

Abstract

There are various forms of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) modeling. The contribution of this study is to propose a class of non-linear AGARCH (Asymmetric GARCH) model by applying the Simple Tukey transformation to the lagged-volatility equation. The model is fitted to the daily returns of buying exchange rate of the USD (US Dollar) to the IDR (Indonesian Rupiah) from January 2010 to December 2017. The Adaptive Random Walk Metropolis (ARWM) method is employed in the Markov chain Monte Carlo algorithm to estimate model parameters. This study finds that both asymmetric effect (between return and volatility) and non-linearity in volatility are statistically significant, suggesting to incorporate both parameters into the GARCH(1,1) model. To choose the better fit model, the Log-likelihood Ratio Test (LRT) and Deviance Information Criterion (DIC) are employed. The empirical results indicate that the proposed model outperforms the basic AGARCH(1,1) model. Therefore, this study suggest a new class of non-linear AGARCH model.