Cassim, Lucius (2018): Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model.

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Abstract
Recently, volatility modeling has been a very active and extensive research area in empirical finance and time series econometrics for both academics and practitioners. GARCH models have been the most widely used in this regard. However, GARCH models have been found to have serious limitations empirically among which includes, but not limited to; failure to take into account leverage effect in financial asset returns. As such so many models have been proposed in trying to solve the limitations of the leverage effect in GARCH models two of which are the EGARCH and the TARCH models. The EGARCH model is the most highly used model. It however has its limitations which include, but not limited to; stability conditions in general and existence of unconditional moments in particular depend on the conditional density, failure to capture leverage effect when the parameters are of the same signs, assuming independence of the innovations, lack of asymptotic theory for its estimators et cetera. This paper therefore is geared at extending/improving on the EGARCH model by taking into account the said empirical limitations. The main objective of this paper therefore is to develop a volatility model that solves the problems faced by the exponential GARCH model. Using the Quasimaximum likelihood estimation technique coupled with martingale techniques, while relaxing the independence assumption of the innovations; the paper has shown that the proposed asymmetric volatility model not only provides strongly consistent estimators but also provides asymptotically efficient estimators
Item Type:  MPRA Paper 

Original Title:  Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model 
English Title:  Modelling asymmetric conditional heteroskedasticity in financial asset returns: an extension of Nelson’s EGARCH model 
Language:  English 
Keywords:  GARCH, TARCH, EGARCH, Quasi Maximum Likelihood Estimation, Martingale 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics 
Item ID:  86615 
Depositing User:  Mr Lucius Cassim 
Date Deposited:  11 May 2018 12:00 
Last Modified:  14 Oct 2019 15:39 
References:  Amemiya, T. (1985). Advanced Econometrics. Cambridge: Havard University Press. Andersen, T. G. (1996). GMM estimation of stochastic volatility models:A monte Carlo Study. Journal of Business and Economic Statistics,48, 328352. Avran, F. (1988). Weak Convergence of the variations,iterated integrals and DoleansDade exponentials of sequences of semimartingales. Anals of probability 16, 246250. Baillie, R. T., & Bollerslev, T. (1987). The message in Daily Exchange Rates: A conditional Variance Tale. Econometrica. Bollerslev. (1987). A conditional Heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics,69, 542547. Bollerslev, T. (1986). Generalized Autoregressive Heteroskedasticity. Journal of Econometrics, 307327. Bollersslev, J., & Woodridge, J. (1992). Quasi maximum likelihood estimation and inference in dynamic models with time varying covariances. Econometric Reviews,11(2), 143172. Buhlman, P., & McNeil, A. J. (2000). Nonparametric GARCH Models. Zurich, Switzerland: Seminar Fur Statistik:CH8092. Cameron, C. A., & Trivedi, P. (2005). Microeconometrics:Methods and Applications. New York,USA: Cambrdge University Press. Choi, E. J. (2004). Estimation of Stochastic Volatility Models by Simulated Maximum Likelihood Method. University of Waterloo. Chung, S. S. (2012). A class of nonparametric volatility models:Application to financial time series. Journal of Econometrics. Dahl, C. M., & Levine, M. (2010). Nonparametric estimation of volatility models under serially dependent innovations. Econometrica. Davidson, J. (2000). Econometric Theory. Blackwel: Oxford University Press. Davidson, R., & Mackinnon, J. (1993). Estimation and inference in Econometrics. London: Oxford University Press. Drost, F. C., & Klasssen, C. (1996). Efficient estimation in Semiparametric GARCH Models. Discussion paper;vol(199638),Tilburg. Duan, J. (1997). Augmented GARCH(p,q) process and its diffusion limit. Journal of Econometrics,79(1), 97127. Engle, R. (1982). Autoregressive Conditional Heteroskedasticity with estimation of the variance of U.K inflation. Econometrica, 9871008. Engle, R. F., & GonzaleRivera, G. (October,1991). Semiparametric ARCH Models. Journal of Business and Economic Statistics, 9(4), 345359. Engle, R. F., & Ng, V. (1993). Measuring and testing the impact of news on volatility. Journal of finance,48, 17471778. Fan, & Gijbels, I. (1995). Datadriven bandwidth selection in local polynomial fitting:variable bandwidth and spatial adaptation. Journal of Royal Statistical Society,B,57, 371394. Fan, J., & Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika,85, 645660. Gallant, A. R., & Hsieh, D. (1989). Fitting a Recalcitrant series:The Pound/Dollar Exchange Rate,197483. Econometrica. Geweke, J. (1986). Modelling Persistence in Conditional Variances: A Comment. Econometric Review,5, 5661. Glosten, L. R., & Runkle, D. (1993). On the relation between the expected value and volatility of the nominal excess return of stocks. Journal of Finance,48, 17791801. Gourieroux, C., & Trognon, A. (1984). Pseudo Maximum Likelihood Methods:Theory,52(1). Econometrica, 681700. Haafner, C. M. (2003). Analytical quasi maximum likelihood inference in BEKKGARCH models. Econometric Institution,Erasmus University,Rotterdam. Hafner, C. M., & Rombonts, J. (2002). Semiparametric multivariate GARCH models . Discussion paper,2002/XX,CORE. Hansen, B. C. (2006). Econometrics. New York: Cambridge University Press. Hansen, P., & Heyde, C. (1980). Martingale limit theory and its applications. New York: Academic Press. Hansen, R. P., & Lunde, A. (2001). A comparison of volatility models:Does anything beat GARCH(1,1)? Centre for analytica finance:University of AARHUS. Hentshel, L. (1995). All in the family: Nesting Symetric and Asymetric GARCH Models. Journal of Financial Economics,39, 71104. Herwartz, H. (2004). ConditionalHeteroskedasticity.In H. Lutkepoh, & M. Kratzig (Eds.) Themes in Modern Econometrics, pp. 197220. Higging, M. L., & Bera, A. (1992). A Class of nonlinear ARCH Models. International Economic Review. Holly. (2009). Modelling Risk using fourth order Pseudo Maximum Likelihood Methods. University of Lausanne, Institute of Healthy Economics. Holly, A., & Montifort, A. (2010). Fourth Order Pseudo Maximum Likelihood Methods. Econometrica. Holly, A., & Pentsak, Y. (2004). Maximum Likelihhod Estimation of the Conditional mean E(YX) for Skewed Dependent variables in FourthParameter families of Distributions. Technical Report, University of Lausanne, Institute of Healthy Economics and Management. Hood, W., & Koopman, T. (1953). The estimation of simultaneous linear economic relationships. Econometric Methods. Ibragimov, R., & Philips, P. (2010). Regression asymptotics using martingale convergence. Yale University press. Kouassi, E. (2015). Consistency of Pseudomaximum likelihood estimation in ARCH(1) under dependent innovations. Working paper. Linton, O., & Mammen, E. (May, 2003). Estimating Semiparametric ARCH(∞) nodels by kernel smoothing methods. Discussion paper,No:EM/03/453. McCullagh, P. (1994). Exponential mixtures and quadratic exponential families. Biometrika, 81(4), 721729. Nadaraya, E. (1964). "On Estimating Regression".The Theory of Probability and its Applications. Econometrica, 1412. Nielsen, B. (1978). Information and exponential families in statiatical theory. New York: Wiley. Pantula, S. G. (1986). Modelling Persistence in Conditional Variances: A comment. Econometric Review,5, 7174. Posedel, P. (2005). Properties and estimation of GARCH(1,1) model. Metodoloski Zvezki, 2, 243257. Rao, C. R. (1973). Linear statistical inference and its applications. New York: John Willey & Sons. Rossi, E. (2004, march). A note on GARCH models. Working paper. Sentana, C. (1995). Quadratic ARCH Models. Review of Economic Studies,62(4), 639661. Sherphard, N. (2008). Statistical aspects of ARCH and Stochastic Volatility. In D. R. Cox, D. Hinkly, & O. Barndorff (Eds) Time series models in Econometrics, Finance and other fields.Monographs on statistics and Applied probability,65, pp. 165. Sousi, P. (2013). Advanced Probability. New York: Cambridge University Press. Stout, W. F. (1974). Almost Sure Convergence. New York: Academic Press. Su, L., Ullah, A., & Mashra, S. (2011). Nonparametric and semiparametric volatility models:specification,estimation and testing. Econometrica. Tapia, R. A., & Thompson, J. (n.d.). Nonparametric Probability Density Estimation. Taylor, S. (1986). Modelling Financial Time Series. John Wiley & Sons. Tsay, R. S. (2010). Analysis of time series. Willey. Tschiernig, R. (2004). Nonparametric Econometrics. In H. Lutkepoh, & M. Kratzig (Eds) Themes in Econometrics, pp. 243289. Watson, G. (1964). Smooth Regression Analysis. The Indian Journal of Statistics, 359372. Weiss, A. A. (1986). Asymptotic Theory for ARCH Models: Estimation and Testing. Econometric Theory,2, 107131. Williams, D. (1991). Probability with martingales. New York: Cambridge University Press. Yang, L., & Song, Q. (2012). Efficient Semiparametric GARCH Modelling of Financial Volatility. Statistica Sinica, 22, 249270. Zakoian, M. J. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control,18, 931955. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/86615 