DOI: https://doi.org/10.14710/medstat.14.1.21-32

SKEW NORMAL AND SKEW STUDENT-T DISTRIBUTIONS ON GARCH(1,1) MODEL

*Didit Budi Nugroho orcid scopus  -  Department of Mathematics and Data Science, Universitas Kristen Satya Wacana, Indonesia
Agus Priyono  -  Department of Mathematics and Data Science, Universitas Kristen Satya Wacana, Indonesia
Bambang Susanto  -  Department of Mathematics and Data Science, Universitas Kristen Satya Wacana, Indonesia
Open Access Copyright (c) 2021 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
The Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) type models have become important tools in financial application since their ability to estimate the volatility of financial time series data. In the empirical financial literature, the presence of skewness and heavy-tails have impacts on how well the GARCH-type models able to capture the financial market volatility sufficiently. This study estimates the volatility of financial asset returns based on the GARCH(1,1) model assuming Skew Normal and Skew Student-t distributions for the returns errors. The models are applied to daily returns of FTSE100 and IBEX35 stock indices from January 2000 to December 2017. The model parameters are estimated by using the Generalized Reduced Gradient Non-Linear method in Excel’s Solver and also the Adaptive Random Walk Metropolis method implemented in Matlab. The estimation results from fitting the models to real data demonstrate that Excel’s Solver is a promising way for estimating the parameters of the GARCH(1,1) models with non-Normal distribution, indicated by the accuracy of the estimation of Excel’s Solver. The fitting performance of models is evaluated by using log-likelihood ratio test and it indicates that the GARCH(1,1) model with Skew Student-t distribution provides the best fitting, followed by Student-t, Skew-Normal, and Normal distributions.
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Keywords: Skew Distribution; GARCH; Excel’s Solver; Volatility
Funding: Universitas Kristen Satya Wacana with Contract Number: 436/Penel./Rek./9/V/2019

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Language : EN
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  1. Abadie, J., & Carpenter, J. (1969). Generalization of the Wolfe Reduced Gradient Method to the Case of Nonlinear Constraints. In R. Fletcher (Ed.), Optimization (pp. 37–47). Academic Press
  2. Abdalla, S. Z. S., & Winker, P. (2012). Modelling Stock Market Volatility Using Univariate GARCH Models: Evidence from Sudan and Egypt. International Journal of Economics and Finance, 4(8), 161–176
  3. Altun, E., Tatlidil, H., Ozel, G., & Nadarajah, S. (2018). Does the Assumption on Innovation Process Play An Important Role for Filtered Historical Simulation Model? Journal of Risk Financial Management, 11(1), 7
  4. Atchade, Y. F., & Rosenthal, J. S. (2005). On Adaptive Markov Chain Monte Carlo Algorithms. Bernoulli, 11(5), 815–828
  5. Azzalini, A. (2011). Skew-normal Distribution. In M. Lovric (Ed.), International encyclopedia of statistical science. Springer Berlin Heidelberg
  6. Azzalini, A., & Capitanio, A. (2003). Distributions Generated by Perturbation of Symmetry with Emphasis on A Multivariate Skew t-Distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2), 367–389
  7. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327
  8. Bollerslev, T. (1987). A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. The Review of Economics and Statistics, 69(3), 542–547
  9. Cerqueti, R., Giacalone, M., & Mattera, R. (2020). Skewed Non-Gaussian GARCH Models for Cryptocurrencies Volatility Modelling. Information Sciences, 527, 1–26
  10. Choi, S. W., & Lam, D. M. H. (2017). Comparing Two Methods-Agreeing to Disagree. Anaesthesia, 72(5), 651–653
  11. Chu, J., Chan, S., Nadarajah, S., & Osterrieder, J. (2017). GARCH Modelling of Cryptocurrencies. Journal of Risk and Financial Management, 10(4), 17
  12. Cifter, A. (2012). Volatility Forecasting with Asymmetric Normal Mixture GARCH Model: Evidence from South Africa. Romanian Journal of Economic Forecasting, 15(2), 127–142
  13. Fernandez, C., & Steel, M. (1998). On Bayesian Modeling of Fat Tails and Skewness. Journal of the American Statistical Association, 93(441), 359–371
  14. Hansen, P. R., & Lunde, A. (2005). A Forecast Comparison of Volatility Models: Does Anything Beat A GARCH(1,1)? Journal of Applied Econometrics, 20(7), 873–889
  15. Iqbal, F., & Triantafyllopoulos, K. (2019). Bayesian Inference of Multivariate Rotated GARCH Models with Skew Returns. Communications in Statistics: Simulation and Computation, 0(0), 1–19
  16. Kusumawati, A. M., Nugroho, D. B., & Sasongko, L. R. (2020). Estimasi volatilitas Melalui Model EGARCH(1,1) Berdistribusi Student-t dan Alpha Skew Normal. Jurnal Ekonomi Kuantitatif Terapan, 13(2), 259–272
  17. Lasdon, L. S., Fox, R. L., & Ratner, M. W. (1974). Nonlinear Optimization Using the Generalized Reduced Gradient Method. Recherche Opérationnelle, 8(3), 73–103
  18. Le, H., Pham, U., Nguyen, P., & Pham, T. B. (2020). Improvement on Monte Carlo Estimation of HPD Intervals. Communications in Statistics - Simulation and Computation, 49(9), 2164–2180
  19. Lee, H., Chen, S., & Kang, H. (2004). A Study of Generalized Reduced Gradient Method with Different Search Directions. Measurement Management Journal, 1(1), 25–38
  20. Maia, A., Ferreira, E., Oliveira, M. C., Menezes, L. F., & Andrade-Campos, A. (2017). Numerical Optimization Strategies for Springback Compensation in Sheet Metal Forming. In Computational Methods and Production Engineering (pp. 51–82)
  21. Metropolis, N., Rosenbluth, A. W., Rosenbluth, N. M., Teller, A. H., & Teller, E. (1953). Equations of State Calculations by Fast Computing Machine. The Journal of Chemical Physics, 21, 1087–1091
  22. Nugroho, D. B. (2018). Comparative Analysis of Three MCMC Methods for Estimating GARCH Models. IOP Conference Series: Materials Science and Engineering, 403(1), 012061
  23. Nugroho, D. B., Kurniawati, D., Panjaitan, L. P., Kholil, Z., Susanto, B., & Sasongko, L. R. (2019). Empirical Performance of GARCH, GARCH-M, GJR-GARCH and log-GARCH Models for Returns Volatility. Journal of Physics: Conference Series, 1307(1), 012003
  24. Nugroho, D. B., & Susanto, B. (2017). Volatility Modeling for IDR Exchange Rate Through APARCH Model with Student-t Distribution. AIP Conference Proceedings, 1868(1), 040005
  25. Nugroho, D. B., Susanto, B., Prasetia, K. N. P., & Rorimpandey, R. (2019). Modeling of Returns Volatility Using GARCH(1,1) Model under Tukey Transformations. Jurnal Akuntansi dan Keuangan, 21(1), 12–20
  26. Nugroho, D. B., Susanto, B., & Pratama, S. R. (2017). Estimation of Exchange Rate Volatility Using APARCH-type Models: A Case Study of Indonesia (2010–2015). Jurnal Ekonomi dan Ekonomi Studi Pembangunan, 9(1), 65–75
  27. Nugroho, D. B., Susanto, B., & Rosely, M. M. M. (2018). Penggunaan MS Excel untuk Estimasi Model GARCH(1,1). Jurnal Matematika Integratif, 14(2), 71–83
  28. Powell, S. G., & Batt, R. J. (2008). Modeling for Insight: A Master Class for Business Analysts. In Modeling for Insight: A Master Class for Business Analysts
  29. Robert, C., & Casella, G. (2011). A Short History of Markov Chain Monte Carlo: Subjective Recollections from Incomplete Data. Statistical Science, 26(1), 102–115
  30. Roberts, G. O., & Rosenthal, J. S. (2009). Examples of Adaptive MCMC. Journal of Computational and Graphical Statististics, 18(2), 349–367
  31. Roussas, G. G. (1997). A Course in Mathematical Statistics. Second Edition. In Academic Press (Vol. 134, Issue 4)
  32. Salim, F. C., Nugroho, D. B., & Susanto, B. (2016). Model Volatilitas GARCH(1,1) dengan Error Student-t untuk Kurs Beli EUR dan JPY terhadap IDR. Jurnal MIPA, 39(1), 63–69
  33. Sartika, Q. R., Widiharih, T., & Mukid, M. A. (2019). Value at Risk Instock Portfolio Using t-Copula. Media Statistika, 12(2), 175–187
  34. Solomon, J. (2015). Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics. CRC Press,
  35. Tyas, M. D. P., Maruddani, D. A. I., & Rahmawati, R. (2019). Perhitungan Value at Risk dengan Pendekatan Threshold Autoregressive Conditional Heteroscedasticity-Generalized Extreme Value. Media Statistika, 12(1), 73–85
  36. Wu, Q., & Vos, P. (2018). Inference and Prediction. In V. N. Gudivada & C. R. Rao (Eds.), Computational Analysis and Understanding of Natural Languages: Principles, Methods and Applications (pp. 131–192). North-Holland

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