Sains Malaysiana 46(1)(2017): 107–116

http://dx.doi.org/10.17576/jsm-2017-4601-14

The HARX-GJR-GARCH skewed-t multipower realized volatility modelling for S&P 500

(Pemodelan Kemeruapan Terealisasi Pelbagai-Kuasa HARX-GJR-GARCH terpencong-t

untuk S&P 500)

CHIN WEN CHEONG¹*, LEE MIN CHERNG², NADIRA MOHAMED ISA^{1 3} & POO KUAN HOONG⁴

¹Faculty of  Management, Multimedia University, 63100 Cyberjaya, Selangor Darul Ehsan, Malaysia

²Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Sungai Long Campus, Jalan Sungai Long, Bandar Sungai Long, 43000 Kajang, Selangor Darul Ehsan, Malaysia

³Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

⁴The Nielsen Company (M) Sdn. Bhd., 46100 Petaling Jaya, Selangor Darul Ehsan, Malaysia

Diserahkan: 8 Oktober 2015/Diterima: 25 April 2016

ABSTRACT

The heterogeneous autoregressive (HAR) models are used in modeling high frequency multipower realized volatility of the S&P 500 index. Extended from the standard realized volatility, the multipower realized volatility representations have the advantage of handling the possible abrupt jumps by smoothing the consecutive volatility. In order to accommodate clustering volatility and asymmetric of multipower realized volatility, the HAR model is extended by the threshold autoregressive conditional heteroscedastic (GJR-GARCH) component. In addition, the innovations of the multipower realized volatility are characterized by the skewed student-t distributions. The extended model provides the best performing in-sample and out-of-sample forecast evaluations.

Keywords: GARCH; HAR; realized volatility

ABSTRAK

Model autoregresi heterogen (HAR) digunakan dalam pemodelan kemeruapan terealisasi pelbagai-kuasa untuk indeks S&P500. Lanjutan daripada kemeruapan terealisasi piawai, kemeruapan pelbagai-kuasa mempunyai kelebihan menangani kemungkinan perubahan mendadak dengan pelicinan kemeruapan berturutan. Untuk permodelan kemeruapan kelompok dan tak simetri, model HAR dilanjutkan dengan komponen autoregresi heteroskedastik bersyarat ambang (GJR-GARCH). Selain itu, inovasi kemeruapan terealisasi dicirikan dengan taburan student-t terpencong. Model lanjutan HAR memberi prestasi terbaik dalam penilaian penganggaran dan ramalan.

Kata kunci: GARCH; HAR; kemeruapan terealisasi

RUJUKAN

Andersen, T.G., Bollerslev, T. & Diebold, F.X. 2006. Roughing it up: Including jump components in the measurement, modeling and forecasting of return volatility. Review of Economics and Statistics 89: 701-720.

Andersen, T. & Bollerslev, T. 1998. Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review 39: 885-906.

Barndorff-Nielsen, O.E., Graversen, S.E., Jacod, J., Podolskij, M. & Shephard, N. 2006. A central limit theorem for realised power and bipower variations of continuous semi-martingales. Journal of Financial Econometrics 2(1): 1-37.

Barndorff-Nielsen, O.E. & Shephard, N. 2002. Estimating quadratic variation using realised volatility. Journal of Applied Econometrics 17: 457-477.

Barndorff-Nielsen, O.E. & Shephard, N. 2004. Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics 2(1): 1-37.

Bollerslev, T. & Ghysels, E. 1996. Periodic autoregressive conditional heteroscedasticity. Journal of Business & Economic 14(2): 139-151.

Cervelló, R.R., Guijarro, F. & Michniuk, K. 2015. Stock market trading rule based on pattern recognition and technical analysis: Forecasting the DJIA index with intraday data. Expert System and Application 42(14): 5963-5975.

Cheong, C.W., Lee, M.C. & Grace Yap, L.C. 2016a. Heterogeneous autoregressive model with structural break using nearest neighbor truncation volatility estimators for DAX. SpringerPlus 5(1883): 1-13.

Cheong, C.W., Lee, M.C. & Grace Yap, L.C. 2016b. Modelling financial market volatility using asymmetric-skewed-ARFIMAX and -HARX models. Inžinerinė Ekonomika 27(4): 373-381.

Cheong, C.W. 2013. The computational of stock market volatility from the perspective of heterogeneous market hypothesis. Economic Computation and Economic Cybernetics Studies and Research 47(2): 247-260.

Corsi, F. 2009. A simple approximate long memory model of realized volatility. Journal of Financial Econometrics 7: 174-196.

Corsi, R., Mittnik, S., Pigorsch, C. & Pigorsch, U. 2008. The volatility of realized volatility. Econometric Reviews 27: 46-78.

Dacorogna, M., Ulrich, M., Richard, O. & Oliveier, P. 2001. Defining efficiency in heterogeneous markets. Quantitative Finance 1: 198-201.

Degiannakis, S. & Floros, C. 2013. Modeling. CAC40 volatility using ultra-high frequency data. Research in International Business and Finance 28: 68-81.

Fama, E. 1998. Market efficiency, long-term returns, and behavioral finance. Journal of Financial Economics 49: 283-306.

Glosten, L.R., Jaganathan, R. & Runkle, D. 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance 8: 1779-1801.

Hong, Y., Li, H. & Zhao, F. 2004. Out-of-sample performance of discrete-time spot interest rate models. Journal of Business & Economic Statistics 22(4): 457-473.

Inkaya, Y. & Oku, Y. 2014. Analysis of volatility feedback and leverage effects on the ISE30 index using high frequency data. Journal of Computational and Applied Mathematics 259: 377-384.

Jorion, P. 2006. Value-at-Risk: The New Benchmark for Controlling Market Risk. 3rd ed. Chicago: McGraw-Hill.

Lambert, P. & Laurent, S. 2001. Modelling financial time Series Using GARCH-Type models and a skewed student density. Mimeo, Universit?e de Li?ege.

Malkiel, B.G. 2003. The efficient market hypothesis and its critics. The Journal of Economic Perspectives 17(1): 59-82.

Muller, U., Dacorogna, M., Dav, R., Olsen, R., Pictet, O. & Ward, J. 1993. Fractals and intrinsic time - a challenge to econometricians. XXXIX-th International AEA Conference on Real Time Econometrics. pp. 14-15.

Patton, A.J. 2011. Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics 160(1): 246-256.

Wang, X., Wu, C. & Xu, W. 2015. Volatility forecasting: The role of lunch-break returns, overnight returns, trading volume and leverage effects. International Journal of Forecasting 31: 609-619.

Zu, Y. & Boswijk, H.P. 2014. Estimating spot volatility with high frequency financial data. Journal of Econometrics 181(2): 117-135.

*Pengarang untuk surat menyurat; email: wcchin@mmu.edu.my