Share This Article:

Composite Likelihood for Bilinear GARCH Model

Abstract Full-Text HTML Download Download as PDF (Size:2508KB) PP. 2311-2317
DOI: 10.4236/am.2014.515225    3,912 Downloads   4,476 Views  

ABSTRACT

In this study, we focus on the class of BL-GARCH models, which is initially introduced by Storti & Vitale [1] in order to handle leverage effects and volatility clustering. First we illustrate some properties of BL-GARCH (1, 2) model, like the positivity, stationarity and marginal distribution; then we study the statistical inference, apply the composite likelihood on panel of BL-GARCH (1, 2) model, and study the asymptotic behavior of the estimators, like the consistency property and the asymptotic normality.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Bouchemella, A. and Benmostefa, F. (2014) Composite Likelihood for Bilinear GARCH Model. Applied Mathematics, 5, 2311-2317. doi: 10.4236/am.2014.515225.

References

[1] Storti, G. and Vitale, C. (2003) BL-GARCH Models and Asymmetries in Volatility. Statistical Methods and Applications, 12, 19-40.
http://dx.doi.org/10.1007/BF02511581
[2] Engle, R.F. (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 987-1007.
http://dx.doi.org/10.2307/1912773
[3] Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327. http://dx.doi.org/10.1016/0304-4076(86)90063-1
[4] Diongue, A.K., Guégan, D. and Wolff, R.C. (2009) BL-GARCH Models with Elliptical Distributed Innovations. Journal of Statistical Computation and Simulation, 80, 775-791.
http://dx.doi.org/10.1080/00949650902773577
[5] Besag, J. (1974) Spatial Interaction and the Statistical Analysis of Latice Systems. Journal of the Royal Statistical Society: Series B, 36, 192-236.
[6] Lindsay, B. (1988) Composite Likelihood Methods. In: Prabhu, N.U., Ed., Statistical Inference from Stochastic Processes, American Mathematical Society, Providence, 221-239.
http://dx.doi.org/10.1090/conm/080/999014
[7] Larribe, F. and Fearnhead, P. (2011) On Composite Likelihoods in Statistical Genetics. Statistica Sinica, 21, 43-69.
[8] Richard, A.D. and Chun, Y.Y. (2011) Comments on Pairwise Likelihood in Time Series Models. Statistica Sinica, 21, 255-277.
[9] Pakel, C., Shephard, N. and Sheppard, K. (2011) Nuisance Parameters, Composite Likelihoods and Panel of GARCH Models. Satistica Sinica, 21, 307-329.
[10] Monlenberghs, G. and Vervbeke, G. (2005) Models for Discrete Longitudinal Data. Springer, New York.
[11] Francq, C. and Zankoian, J.M. (2010) GARCH Models. Wiley, Hoboken.
http://dx.doi.org/10.1002/9780470670057
[12] Engle, R.F. and Mezrich, J. (1996) GARCH for Groups. Risk, 9, 36-40.
[13] Engle, R.F., Shephard, N. and Sheppard, K. (2008) Fitting Vast Dimensional Time-Varying Covariance Models. Working Paper.
[14] Engle, R.F., Hendry, D.F. and Richard, J.F. (1983) Exogeneity. Econometrica, 51, 277-304.
http://dx.doi.org/10.2307/1911990
[15] Wu, B., Yao, Q. and Zhu, S. (2013) Estimation in the Presence of Many Nuisance Parameters: Composite Likelihood and Plug-In Likelihood. Stochastic Processes and Their Applications, 123, 2877-2896.
http://dx.doi.org/10.1016/j.spa.2013.03.017

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.