Bayesian Estimation of Generalized Auto Regressive Conditionally Heteroscedastic Model with an Application to Foolad Mobarakeh Stock Returns

Volume 8, Issue 3, pp 297-306 http://dx.doi.org/10.22436/jmcs.08.03.12

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2352 Downloads
• 3550 Views

Authors

Hoda Nazari - Department of Statistics, Faculty of Sciences, Golestan University, Gorgan, Golestan, Iran. Manoochehr Babanezhad - Department of Statistics, Faculty of Sciences, Golestan University, Gorgan, Golestan, Iran. Majid Azimmohseni - Department of Statistics, Faculty of Sciences, Golestan University, Gorgan, Golestan, Iran.

Abstract

Problems in economics and finance have recently motivated the study of the volatility of a time series data setting. Several time series models to concern the volatility of such data have been considered. Although the Auto Regressive Moving Average (ARMA) models assume a constant variance, models such as the Auto Regressive Conditionally Heteroscedastic (ARCH) models are developed to the model changes in volatility. In this paper, we indicate that the generalized ARCH (GARCH) models which have been proposed are useful in many economics and financial studies. We thus develop both probabilistic properties and the Bayesian estimation method of a GARCH (1, 1) model. We then illustrate the model on Foolad Mobarakeh (F.M) daily returns from 2007 to 2012. Further we forecast future values of conditional variance of returns.

Share and Cite

Keywords

• ARCH
• GARCH
• Heteroscedastic
• Volatility
• Metropolis-Hasting algorithm.

MSC

•  91G70
•  62P05
•  62F15

References

• [1] V. Akgiray, Conditional heteroskedasticity in time series of stock returns: evidence and forecasts, Journal of Business, 62 (1989), 55-80.
  • Google Scholar


• [2] T. G. Andersen, T. Bollerslev, P. F. Christoffersen, F. X. Diebold, Volatility and Correlation Forecasting, in G. Elliot, C.W.J. Granger, and A. Timmermann, Handbook of Economic Forecasting, Amsterdam, North-Holland, (2006), 778-878.
  • View Article
  • Google Scholar


• [3] M. Babanezhad, Trend Analysis with Effective Covariates Based On Auto Regressive Moving Average Time Series Residuals, journal of mathematics and computer science, 7 (2013), 121-130.
  • Google Scholar


• [4] T. Bollerslev, Generalized Autoregressive Conditional Heteroskedasticity, journal of Econometrics, 31 (1986), 307-327.
  • View Article
  • Google Scholar


• [5] P. J. Deschamps , A Flexible Prior Distribution for Markov Switching Autoregressions with Student-t Errors, Journal of Econometrics, 133(1) (2006), 153-190.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] R. F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, journal of Econometrica, 50 (1982), 987-1007.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] J. Fan, Q. Yao, Nonlinear time series: nonparametric and parametric methods, Springer, New York (2003)
  • Google Scholar


• [8] A. Ghalanos, rgarch: Flexible GARCH modelling in R, URL http://r-forge.r-project.org/projects/rgarch. , (2010)
  • Google Scholar


• [9] L. Giraitis, P. Kokoszka, R. Leipus, Stationary ARCH models: dependence structure and central limit theorem, Economet. Theory , 16 (2000), 3-22.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] T. Nakatsuma, A markov-chain sampling algorithm for GARCH models, Studies in Nonlinear Dynamics and Econometrics, 3(2) (1998), 107–117.
  • View Article
  • Google Scholar


• [11] S.-H. Poon, C. Granger, Forecasting Volatility in Financial Markets: A Review, Journal of Economic Literature, 41(2) (2003), 478-539.
  • View Article
  • Google Scholar


• [12] S.-H. Poon, C. Granger, Practical Issues in Forecasting Volatility, Financial Analysts Journal, 61(1) (2005), 45-56.
  • View Article
  • Google Scholar


• [13] R. H. Shumway, D. S. Stoffer, Time Series Analysis and Its Applications: With R Examples, Springer, (2010)
  • View Article
  • Google Scholar
  • MATH


• [14] A. Silvennoinen, T. Teräsvirta, Multivariate GARCH, In T.G. Andersen, R.A. Davis, J-P Kreiss and T. Mikosch, editors, Handbook of Financial Time Series, Springer, New York (2008)
  • Google Scholar


• [15] A. Trapletti, K. Hornik, tseries: Time series analysis and computational finance, URL http: //CRAN.R-project.org/package=tseries. , (2009)
  • Google Scholar


• [16] T. Teräsvirta, An Introduction to Univariate GARCH Models, In T.G. Andersen, R.A. Davis, J-P Kreiss, and T. Mikosch, editors, Handbook of Finananccial Time Series, New York, Springer, (2008), 17-42.
  • View Article
  • Google Scholar
  • MATH


• [17] D. Wuertz, Y. Chalabi, fGarch: Rmetrics-Autoregressive Conditional Heteroskedastic Modelling, URL http://CRAN.R-project.org/package=fGarch., (2009)
  • Google Scholar