Email this article Parameters estimation for GARCH (p,q) model: QL and AQL approaches
Abstract
In this paper, estimation for the generalized autoregressive conditional heteroscedasticity (GARCH) model is conducted. The Quasi likelihood (QL) and Asymptotic Quasi-likelihood (AQL) estimation methods are suggested in this paper. The QL approach relaxes the distributional assumptions of GARCH processes. The AQL technique obtains out the QL method when the conditional variance of process is unknown.
The AQL methodology, merging the kernel technique used for parameter estimation of the GARCH model. This AQL methodology enables a substitute technique for parameter estimation when the conditional variance of process is unknown. Application of the QL and AQL methods to weekly prices changes of crude oil modelled by GARCH model is considered.
References
T. Bollerslev. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31(3):307–327, 1986.
R.F. Engle. Autoregressive conditional heteroskedasticity with estimates of the variance of u.k. inflation. Econometrica, 50:987–1008, 1982.
R.Y. Chou Bollerslev, T. and K.F. Kroner. Arch modeling in finance: A selective review of the theory and empirical evidence. Journal of Econometrics, 52:5–59, 1992.
R.F. Engle. Garch 101: The use of arch/garch models in applied econometrics. Journal of Economic Perspectives, 15:157–168, 2001.
F.X. Diebold and J. Lopez. Macroeconometrics: Developments, Tensions and Prospects, chapter Modeling Volatility Dynamics, in K. Hoover (ed.), pages 427–472. Boston: Kluwer Academic Press, 1995.
A. Pagan. The econometrics of financial markets. Journal of Empirical Finance, 3:15–102, 1996.
F. Palm. Handbook of Statistics, volume 14, chapter GARCH Models of Volatility, in C.R. Rao and G.S. Maddala (eds.), pages 209–240. Amsterdam: North-Holland, 1996.
T.G. Andersen and T. Bollerslev. Encyclopedia of Statistical Sciences, volume Vol.II, chapter ARCH and GARCH Models, in S. Kotz, C.B. Read and D.L. Banks (eds). New York: John Wiley and Sons., 1998.
R.F. Engle and A.J. Patton. What good is a volatility model? Quantitative Finance, 1:237–245, 2001.
T. Bollerslev P. Christoffersen Andersen, T.G. and F.X. Diebold. Handbook of Economic Forecasting, chapter Volatility and Correlation Forecasting, in C.W.J. Granger, G.Elliott and A. Timmermann (eds), pages 777–878. Amsterdam: North-Holland., 2006.
C. Alexander. Market Models: A Guide to Financial Data Analysis. Chichester, UK: John Wiley and Sons, Ltd., 2001.
W. Enders. Applied Econometric Time Series. Hoboken, NJ: John Wiley and Sons, Inc., 2004.
S.J. Taylor. Asset Price Dynamics and Prediction. Princeton, NJ: Princeton University Press, 2004.
A. A. Weiss. Asymptotic theory for arch models: estimation and testing. Econometric Theory, 2(1):107–131, 1986.
T. Bollerslev and J. M.Wooldridge. Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews, 11(2):143–172, 1992.
Sofia Anyfantaki and Antonis Demos. Estimation and properties of a time-varying gqarch(1,1)-m model. Journal of Probability and Statistics, 2011:39 pages, 2011. Article ID 718647.
Oliver B. Linton and Yang Yan. Semi- and nonparametric arch processes. Journal of Probability and Statistics, 2011:17 pages, 2011. Article ID 906212.
L. Yang. A semiparametric garch model for foreign exchange volatility. Journal of Econometrics, 130(2):365–384, 2006.
O. Linton, J. Pan, and H. Wang. Estimation for a nonstationary semi-strong garch(1, 1) with heavy-tailed errors. Econometric Theory, 26(1):1–28, 2010.
Jianqing Fan, Lei Qi, and Dacheng Xiu. Quasi-maximum likelihood estimation of garch models with heavy tailed likelihoods. J. Bus. Econom. Statist., 32(2):178., 2014.
C. C. Hedye. Quasi-likelihood and its Application: a General Approach to Optimal Parameter Estimation. Springer, New York, 1997.
Y.-X. Lin. A new kind of asymptotic quasi-score estimating function. Scandinavian Journal of Statistics, 27:97–109, 2000.
W. Härdle. Applied Nonparametric Regression. Cambridge, University Press, 1990.
M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall, New York, 1995.
R. Alzghool and Y.-X. Lin. Parameters estimation for ssms: Ql and aql approaches. IAENG International Journal of Applied Mathematics, 38:34–43, 2008.
R. Alzghool and Y.-X. Lin. Initial values in estimation procedures for state space models (ssms). In Proceedings of World Congress on Engineering, London, UK, July 6-8 2011. WCE 2011.
R. Alzghool. Estimation for stochastic volatility model: Quasi-likelihood and asymptotic quasi-likelihood approaches. Journal of King Saud University - Science, in press, 2016.
R. Alzghool and Loai M. Al-Zubi. Semi-parametric estimation for ARCH models. Alexandria Engineering Journal, in press, 2016.
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