From Discrete to Continuous: Modeling Volatility of the Istanbul Stock Exchange Market with GARCH and COGARCH

Yildirim, Yavuz and Unal, Gazanfer (2010): From Discrete to Continuous: Modeling Volatility of the Istanbul Stock Exchange Market with GARCH and COGARCH.

Abstract

The objective of this paper is to model the volatility of Istanbul Stock Exchange market, ISE100 Index by ARMA and GARCH models and then take a step further into the analysis from discrete modeling to continuous modeling. Through applying unit root and stationary tests on the log return of the index, we found that log return of ISE100 data is stationary. Best candidate model chosen was found to be AR(1)~GARCH(1,1) by AIC and BIC criteria. Then using the parameters from the discrete model, COGARCH(1,1) was applied as a continuous model.

• Item Type: MPRA Paper
• Language: English
• Keywords: ISE100,IMKB100,GARCH Modeling,COGARCH Modeling,discrete modeling,continuous modeling
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General

References

1. Barndorff-Nielsen 0. E., Normal Inverse Gaussian Processes and the Modelling of Stock Returns, Research Report 300, Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, 1995 2. Blzsild P., Lecture given at workshop on stochastic processes and financial markets, Personal communication, 1995 3. Bollerslev T., Generalised autoregressive conditionally heteroscedasticity, J. Econometrics, 31:307--327, 1986 4. Dickey O.A. and Fuller W.A., Distribution for the estimates for auto-regressive time series with a unit root, J. Amer. Statist. Assoc., 74:427--431, 1979 5. Duan, J.C., Augmented GARCH(p; q) process and its diffusion limit, J. Econometrics,79-97, 1997 6. Engle R.F., Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation, Econometrica, 50:987--1007, 1982 7. Klüppelberg C., Lindner A., and Maller R., A continuous time GARCH process driven by a Levy process: stationarity and second order behavior, J. Appl. Prob.,41(3):601--622, 2004 8. Maller, R.A., Müller, G. and Szimayer, A., GARCH modelling in continuous time for irregularly spaced time series data, Bernoulli 14(2) 519–542,2008 9. Müller, G., Durand, R., Maller, R., Klüppelberg, C., Analysis of stock market volatility by continuous-time GARCH models, [in]: Gregoriou, G.N., Stock Market Volatility,Chapman Hall/Taylor and Francis, London, pp. 31-50, 2009 10. Nelson D. B., ARCH models as diffusion approximations, J. Econometrics, 45:7--38,1990 11. Taylor S. J., Financial returns modelled by the product of two stochastic processes: a study of daily sugar prices 1961-79. In O. D. Anderson, editor, Time Series Analysis:Theory and Practice, volume 1, pages 203--226. North-Holland, Amsterdam, 1982