International Journal of Mathematics Trends and Technology
Volume 65 | Issue 3 | Year 2019 | Article Id. IJMTT-V65I3P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I3P511
The specification and misspecification of a new class of volatility model that is robust to jumps and outliers is investigated via Monte Carlo experiment and real life examples. The class includes the Generalized Autoregressive Score (GAS) model derived from the classical Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The Exponential GAS (EGAS) and Asymmetric Exponential GAS (AEGAS) models form the variants of the GAS model. Using three different levels of volatility persistence and GARCH probability distributions which are Normal (N), Student-t (T) and Skewed-Student-t (SKT), with estimates of Akaike Information Criterion (AIC) and kurtosis as criteria, we obtained useful information for studying the misspecification and tail behaviour of the newly proposed volatility model. The results of the Monte Carlo experiment, the crude oil and gas prices showed that the best misspecified model for AEGAS-SKT and EGAS-T is EGAS-SKT.
[1] Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31: 307–327.
[2] Harvey, A. (2013). Dynamic Models for volatility and Heavy tails: with applications to financial and economic time series. Cambridge University Press, London.
[3] Harvey, A. and Chakravarty, T. (2008). Beta-t-(E)GARCH. Working paper series.University of Cambridge.
[4] Mandelbrot, B. (1963). The Variation of Certain Speculative Prices. Journal of Business: 36, 394-419.
[5] Fama, E.F. (1970). Efficient Capital Markets: A Review and Theory and Emperical Work. The Journal of Finance: 25, 383-417.
[6] Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom.Econometrica, 50, 987-1008.
[7] Xekalaki, E. and Degiannakis, S. (2010). ARCH Models for Financial Applications.John Wiley and Sons Ltd.
[8] Andersen, T., Bollerslev, T. andDiebold, F.(2007). Roughing itup: including jump components in the measurement, modelling and forecastingof return volatility.The Review of Economics and Statistics: 89, 701–720.
[9] Creal, D., Koopman, S.J. and Lucas, A. (2008). A General Framework for Observation Driven Time-Varying Parameter Models.Tinbergen Institute Discussion Paper.TI 2008-108/4.
[10] Creal, D., Koopman, S. J., and Lucas, A. (2011). A dynamic multivariate heavy-tailed model for time-varying volatilities and correlations. Journal of Business and Economic Statistics: 29, 552-563.
[11] Creal, D., Koopman, S.J. and Lucas, A. (2013). Generalized Autoregressive Score (GAS) Models With Applications. Journal of Applied Econometrics: 28,777-795.
[12] Elder, J., Miao, H. and Ramchander, S. (2013). Jumps in Oil Prices: The role of economic news. The Energy Journal: 34, 217-237.
[13] Charles, A. and Darne, O. (2014). Volatility persistence in Crude oil markets. Energy Policy: 65, 729-742.
[14] Halunga, A.G. and Orme, C.D. (2004). Misspecification tests for GARCH models. School of Social Sciences, University of Manchester, Working Paper, 1-35.
[15] Engle, R.F. and Ng, V.K. (1993). Measuring and Testing the Impact of News on Volatility. The Journal of Finance: 48, 1749-1778.
[16] Lundbergh and Terasvirta (2002). Evaluating GARCH Models. Journal of Econometrics: 110, 417-435.
[17] Posedel, P. (2005). Properties and Estimation of GARCH (1,1) model. MetodoloskiZvezki: 2,243-257.
[18] Bellini, F. and Bottolo, L. (2007). Misspecification and domain issues in fitting Garch (1,1) models: a Monte Carlo investigation. Working paper.University of Milano-Bicocca, Italy and Imperial College London, UK.
[19] Caporin, M. and Lisi, F. (2010). Misspecification tests for periodic long memory GARCH models. Statistical Method and Application: 19, 47-62.
[20] Blasques, F., Koopman, S.J. and Lucas, A. (2008). Stationarity and Ergodicity of Univariate GAS Process. Electronic Journal of Statistics: 8, 1088-1112.
[21] Calvori, F., Cipollini, F. and Gallo, G.M. (2013). Go with the flow: A GAS model for predicting intra-daily volume shares. Social Science Research Network.http://ssrn.com/abstract=2363483
[22] Huang, Z., Wang, T. and Zhang, X. (2014). GAS model with realized measures of volatility.http://ssrn.com/abstract=2461831.
[23] Blasques, F., Koopman, S.J. and Lucas, A. (2014a). Maximum Likelihood Estimation for correctly specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties. Tinbergen Institute Discussion Paper No TI 2014-074/III.
[24] Blasques, F., Koopman, S. J., and Lucas, A. (2014b). Information theoretic optimality of observation driven time series models.Discussion Paper Tinbergen Institute TI 14-046/III.
[25] Bernadi, M. and Cantania, L. (2015a). Switching-GAS copula models for systemic Risk Assessment. arxiv.org/abs/1504.03733vi.
[26] Akaike, H. (1973). “Information theory and an extension of the maximum likelihood principle”. In B.N. Petrov and F. Csaki (eds), Proceedings of the Second International Symposium on Information Theory, pp. 267–281. Budapest: AkademiaiKiado´. Reproduced in S. Kotz and N.L. Johnson (eds), Breakthroughs in Statistics Vol I Foundations and Basic Theory, pp. 610–624. New York: Springer-Verlag 1992.
[27] Nelson, D. B. 1991. “Conditional Heteroscedasticity in Asset Returns: A New approach.” Econometrica: 59, 347–70.
[28] Bauwens, L., Hafner, C. and Laurent, S. (2012). Volatility Models, In Handbook of Volatility Models and Their Applications (eds L. Bauwens, C. Hafner and S. Laurent), John Wiley and Sons, Inc., NJ, U.S.A.
Oluwagbenga T. Babatunde, OlaOluwa S. Yaya, Damola M. Akinlana, "Misspecification of Generalized Autoregressive Score Models: Monte Carlo Simulations and Applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 3, pp. 72-80, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I3P511
PDF 
Abstract 
Keywords 
References 
Citation