Volatility Fitting Performance of QGARCH(1,1) model with Student-t, GED, and SGED Distributions


  • Didit Budi Nugroho Department of Mathematics & Data Science, Universitas Kristen Satya Wacana
  • Bintoro Ady Pamungkas Department of Mathematics & Data Science, Universitas Kristen Satya Wacana
  • Hanna Arini Parhusip Department of Mathematics & Data Science, Universitas Kristen Satya Wacana




volatility fitting performance, Quadratic Generalized Autoregressive Conditional Heteroscedasticity (QGARCH), Student-t, General Error Distribution (GED), Skew GED (SGED)


The research had two objectives. First, it compared the performance of the Generalized Autoregressive Conditional Heteroscedasticity (1,1) (GARCH) and Quadratic GARCH (1,1) (QGARCH)) models based on the fitting to real data sets. The model assumed that return error follows four different distributions: Normal (Gaussian), Student-t, General Error Distribution (GED), and Skew GED (SGED). Maximum likelihood estimation was usually employed in estimating the GARCH model, but it might not be easily applied to more complicated ones. Second, it provided two ways to evaluate the considered models. The models were estimated using the Generalized Reduced Gradient (GRG) Non-Linear method in Excel's Solver and the Adaptive Random Walk Metropolis (ARWM) in the Scilab program. The real data in the empirical study were Financial Times Stock Exchange Milano Italia Borsa (FTSEMIB) and Stoxx Europe 600 indices over the daily period from January 2000 to December 2017 to test the conditional variance process and see whether the estimation methods could adapt to the complicated models. The analysis shows that GRG Non-Linear in Excel's Solver and ARWM methods have close results. It indicates a good estimation ability. Based on the Akaike Information Criterion (AIC), the QGARCH(1,1) model provides a better fitting than the GARCH(1,1) model on each distribution specification. Overall, the QGARCH(1,1) with SGED distribution best fits both data.

Author Biographies

Didit Budi Nugroho, Department of Mathematics & Data Science, Universitas Kristen Satya Wacana

Department of Mathematics & Data Science

Bintoro Ady Pamungkas, Department of Mathematics & Data Science, Universitas Kristen Satya Wacana

Department of Mathematics & Data Science

Hanna Arini Parhusip, Department of Mathematics & Data Science, Universitas Kristen Satya Wacana

Department of Mathematics & Data Science


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