Volatilite Değerleme ve Tahmini Için ARCH ve GARCH Modellerinin Kullanımı

Öz

Bu çalışma, 9 yıllık günlük verilere dayanarak IMKB 100 endeksinin volatilitesini değerlendirmek ve tahmin etmek için, her biri dört ayrı dağılımla denenen, ARMA özellikleri eklenebilen 11 değişik ARCH modelinin performansını sunmaktadır. Elde edilen sonuçlara göre, aynı dağılım kullanılırsa, kısmi entegre edilmiş asimetrik modeller bu özelliğe sahip olmayan orjinal versiyonlarından daha iyi volatilite değerlemesi yapabilmektedir. Çarpık-t ve Student-t dağılımlarının kullanılması modelin veriye daha uyumlu olmasını sağlamaktadır. Sonuç olarak, belirli bir model veya dağılımın kullanılmasının volatilite tahmininde açık bir iyileşmeye yol açmadığı gözlenmiştir.

Anahtar Kelimeler

• GARCH, EGARCH, GJR, APARCH, IGARCH, FIGARCH, FIAPARCH, FIEGARCH, HYGARCH, ARMA, GED, Skewed-t, Ox, G@RCH

The Use of ARCH and GARCH Models for Estimating and Forecasting Volatility

Öz

This paper presents the performance of 11 ARCH-type models each with four different distributions combined with ARMA specifications in conditional mean in estimating and forecasting the volatility of IMKB 100 stock indices, using daily data over a 9 years period. The results suggest that fractionally integrated asymmetric models outperform the non-FI versions and, using skewed-t and student-t distributions provide better fit to the data for almost every model in estimating volatility. In forecasting volatility a clear improvement is not observed by altering a specific model component or distribution

Anahtar Kelimeler

• GARCH, EGARCH, GJR, APARCH, IGARCH, FIGARCH, FIAPARCH, FIEGARCH, HYGARCH, ARMA, GED, Skewed-t, Ox, G@RCH

Kaynakça

1. Baillie, R., T. Bollerslev, and H. Mikkelsen (1996): “Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 74, 3–30., December 17, 2004. http://www.sciencedirect.com
2. Bhardwaj, G. and Swanson, N. R. (2004): “An Empirical Investigation of the Usefulness of ARFIMA Models for Predicting Macroeconomic and Financial Time Series” Special issue of the Journal of Econometrics on “Empirical Methods in Macroeconomics and Finance”., November 15, 2004. ftp://snde.rutgers.edu/Rutgers/wp/2004-22.pdf
3. Bollerslev, T. (1986): “Generalized autoregressive condtional heteroskedasticity,” Journal of Econometrics, 31, 307–327., September 20, 2004. http://www.sciencedirect.com
4. Bollerslev, T., and H. O. Mikkelsen (1996): “Modeling and Pricing Long-Memory in Stock Market Volatility,” Journal of Econometrics, 73, 151–184., December 7, 2004. http://www.sciencedirect.com
5. Chung, C. F. (1999): “Estimating the fractionnally intergrated GARCH model,” National Tai- wan University working paper, December 17, 2004. http://gate.sinica.edu.tw/~metrics/Pdf_Papers/Figarch.pdf
6. Davidson, J. (2001): “Moment and Memory Properties of Linear Conditional Heteroscedas- ticity Models,” Manuscript, Cardiff University, January 4, 2005. http://www.ex.ac.uk/~jehd201/hygarch4.pdf
7. Ding, Z., C. W. J. Granger, and R. F. Engle (1993): “A Long Memory Property of Stock Mar- ket Returns and a New Model,” Journal of Empirical Finance, 1, 83–106., September 20, 2004. http://www.sciencedirect.com
8. Doornik, J. A. (1999): AnObject Oriented Matrix Programming Language. Timberlake Con- sultant Ltd., third edn., Ox Documentation.

9. Doornik, J., and M. Ooms (1999): “A Package for Estimating, Forecasting and Simulating ARFIMA Models: Arfima Package 1.0 for Ox,” Nuffield College (Oxford) discussion pa- per, January 4, 2005. http://www.doornik.com/download/arfima.pdf
10. Engle, R. (1982): “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation,” Econometrica, 50, 987–1007., December 7, 2004. http://www.sciencedirect.com
11. Engle, R., and T. Bollerslev (1986): “Modeling the Persistence of Conditional Variances,” Econometric Reviews, 5, 1–50., December 17, 2004. http://www.sciencedirect.com
12. Glosten, L., R. Jagannathan, and D. Runkle (1993): “On the relation between expected re- turn on stocks,” Journal of Finance, 48, 1779–1801., November 15, 2004. http://www.sciencedirect.com
13. Holton, G. (1996): “Contingency Analysis” family of websites including a riskglossary, No- vember 10, 2004 http://www.contingencyanalysis.com, www.riskglossary.com
14. Laurent, S., and J. P. Peters (2002): “A tutorial for G@RCH 2.3: a complete Ox Package for Estimating and Forecasting ARCH Models,” G@RCH 3.0 documentation.
15. Lambert, P., and S. Laurent (2001): “Modelling Financial Time Series Using GARCH-Type Models and a Skewed Student Density,” Mimeo, Universite de Liege., November 10, 2004. http://www.core.ucl.ac.be/~laurent/pdf/Lambert-Laurent.pdf
16. McKenzie, M. and Mitchell, H. (2001): “Generalised Asymetric Power ARCH Modelling of Exchange Rate Volatility” Royal Melbourne Institute of Technology discussion paper, January 4, 2005. http://mams.rmit.edu.au/mmt5alsrzfd2.pdf
17. Mina, J. and Xiao, J..Y. (2001): “Return to RiskMetrics: The Evolution of a Standard” Copy- right © 2001 RiskMetrics Group. Update and restatement of the mathematical models in the 1996 RiskMetrics Technical Document, November 2, 2004. http://www.riskmetrics.com
18. Nelson, D. (1991): “Conditional heteroskedasticity in asset returns: a new approach,” Econometrica, 59, 349–370., December 7, 2004. http://www.sciencedirect.com
19. Peters, J.P. (2001) “Estimating and Forecasting Volatility of Stock Indices Using Asym- metric GARCH Models and Skewed Student-t Densities,” Working Paper, École d'Ad- ministration des Affaires, University of Liège, Belgium, January 3, 2005. http://www.panagora.com/2001crowell/2001cp_50.pdf
20. Tse, Y. (1998): “The Conditional Heteroscedasticity of the Yen-Dollar Exchange Rate,” Journal of Applied Econometrics, 193, 49–55., http://qed.econ.queensu.ca:80/jae/1998-v13.1/ by http://ideas.repec.org November 10, 2004.
21. Zakoian, J. M. (1994): “Threshold Heteroscedastic Models,” Journal of Economic Dynamics
22. and Control, 18, 931–955., November 10, 2004. http://papers.ssrn.com
23. Zemke, S. (2003): “Data Mining for Prediction. Financial Series Case” The Royal Institute of Technology Department of Computer and Systems Sciences Doctoral Thesis, Decem- ber 4, 2004. http://szemke.math.univ.gda.pl/zemke2003PhD.pdf