Publication: On the Invertibility of EGARCH(p,q)
Loading...
Files
Official URL
Full text at PDC
Publication Date
2015
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Citations
Exportar
Abstract
Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH(p,q) parameters.
Description
The authors are grateful to the Editor-in-Chief, Rob Taylor, an Associate Editor and two referees for very helpful comments and suggestions, and to Christian Hafner for insightful discussions. For financial support, the first author wishes to thank the National Science Council, Taiwan, and the second author is most grateful to the Australian Research Council and the National Science Council, Taiwan.
UCM subjects
Unesco subjects
Keywords
Citation
Black, F. (1976), Studies of stock market volatility changes, 1976 Proceedings of the American Statistical Association, Business and Economic Statistics Section, pp. 177-181.
Bollerslev, T. (1986), Generalised autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, 307-327.
Demos, A. and D. Kyriakopoulou (2014), Asymptotic normality of the QMLEs in the EGARCH(1,1) model. Available online: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2236055 (accessed on 14 June 2014).
Engle, R.F. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007.
Glosten, L., R. Jagannathan and D. Runkle (1992), On the relation between the expected value and volatility of nominal excess return on stocks, Journal of Finance, 46, 1779-1801.
Marek, T. (2005), On invertibility of a random coefficient moving average model, Kybernetika, 41(6), 743-756.
McAleer, M. (2014), Asymmetry and leverage in conditional volatility models, Econometrics, 2(3), 145-150.
McAleer, M., F. Chan and D. Marinova (2007), An econometric analysis of asymmetric volatility: Theory and application to patents, Journal of Econometrics, 139, 259-284.
McAleer, M. and C. Hafner (2014), A one line derivation of EGARCH, Econometrics, 2(2), 92-97.
Nelson, D.B. (1990), ARCH models as diffusion approximations, Journal of Econometrics, 45, 7-38.
Nelson, D.B. (1991), Conditional heteroskedasticity in asset returns: A new approach, Econometrica, 59, 347-370.
Tsay, R.S. (1987), Conditional heteroscedastic time series models, Journal of the American Statistical Association, 82, 590-604.
Straumann, D. and T. Mikosch (2006), Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equation approach, Annals of Statistics, 34, 2449–2495.
Wintenberger, O. (2013), Continuous invertibility and stable QML estimation of the EGARCH(1,1) model, Scandinavian Journal of Statistics, 40, 846–867.