Politická ekonomie 2014, 62(1):100-116 | DOI: 10.18267/j.polek.939

Neparametrický heuristický přístup k odhadu modelu GARCH-M a jeho výhody

Jaromír Kukal, Tran Van Quang
1 České vysoké učení technické.
2 Vysoká škola ekonomická v Praze.

Estimating a GARCH-M Model by a Non-Parametric Heuristic Method and Its Advantages

The models from the GARCH family are often estimated by maximum likelihood method, either parametrically or non-parametrically. Since the parametric estimation procedure is based on an a priori distribution, its misspecification can lead to the inconsistency of the estimators. Therefore non-parametric approach, in which both model's parameters and the distribution of error terms are estimated from the data, seems to be a better alternative. In our work, we propose a non-parametric technique with the use of a heuristic called differential evolution to estimate the parameters of a GARCH-M model. This technique can more likely reach to a global solution of maximum likelihood estimation (MLE) task. Further, it can also more effectively control the required properties of the estimates. The suitability of our approach is verified on modeling the CZK/USD and CZK/EURO forward exchange rate premium of period from 2007 to 2012 by a GARCH-M model.

Keywords: GARCH-M model, Non-parametric method, heuristic, forward risk premium
JEL classification: C14, C61, F31

Published: February 1, 2014  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
Kukal, J., & Van Quang, T. (2014). Estimating a GARCH-M Model by a Non-Parametric Heuristic Method and Its Advantages. Politická ekonomie62(1), 100-116. doi: 10.18267/j.polek.939
Download citation

References

  1. BAILLIE, R. T.; BOLLERSLEV, T. 2000. The Forward Premium Anomaly Is Not as Bad as You Think. Journal of International Money and Finance. 2000, Vol. 19, pp. 471-488. Go to original source...
  2. BEKAERT, G. 1994. Exchange Rate Volatility and Deviation from Unbiasedness in a Cash-inAdvance Model. Journal of International Economics. 1994, Vol. 36, pp. 29-52. Go to original source...
  3. BERNDT, E.; HALL, B.; HALL, R.; HAUSMAN, J. 1974. Estimation and Inference in Nonlinear Structural Models. Annals of Economic and Social Measurement. Vol. 3, No. 4, pp. 653-665.
  4. BHAR, R.; CHIARELLA, C.; PHAM T. 2001. Modelling the Currency Forward Risk Premium: A New Perspective. Asia-Pacific Financial Markets. 2001, Vol. 8, No. 4, pp. 341-360. Go to original source...
  5. BÜHLMANN, P.; MCNEIL, A. J. 2002. An Algorithm for Nonparametric GARCH Modelling. Journal of Computational Statistics and Data Analysis. 2002, Vol. 40, pp. 665-683. Go to original source...
  6. BOLLERSLEV, T. 1986. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics. 1986, Vol. 31, No. 4, pp. 307-327. Go to original source...
  7. DOMOWITZ, I.; HAKKIO, C. S. 1985. Conditional Variance and the Risk Premium in the Foreign Exchange Market. Journal of International Economics. Vol. 19, pp. 47-66. Go to original source...
  8. ENGLE, R. F. 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica. Vol. 50, No. 4, pp. 987-1007. Go to original source...
  9. ENGEL, C. 1996. The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence. Journal of Empirical Finance. Vol. 3, No. 2, pp. 123-192. Go to original source...
  10. ENGLE, R. F.; LILIEN, D.; ROBINS, A. 1987. Estimating Time Varying Risk Premia in the Term Structure: The ARCH-M Model. Econometrica. March 1987, Vol. 55, pp. 391-407. Go to original source...
  11. FILAČEK, J.; KAPIČKA, M.; VOŠVRDA, M. 1998. Testování hypotézy efektivního trhu na BCPP. Finance a úvěr. 1998, Vol. 48, No. 9, pp. 554-566.
  12. HAI, W.; MARK, N. C.; WU, Y. 1997. Understanding Spot-Forward Exchange Rate Regressions. Journal of Applied Econometrics. 1997, Vol. 12, pp.715-734. Go to original source...
  13. HAMILTON, J. D. 1994. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
  14. HANSEN, P. R.; LUNDE, A. 2005. A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1). Journal of Applied Econometrics. 2005, Vol. 20, pp. 873-89. Go to original source...
  15. HARDLE, W. 1992. Applied Nonparametric Regression. Cambridge, UK: Cambridge University Press, 1992.
  16. KOČENDA, E.; POGHOSYAN, T. 2010. Exchange Rate Risk in Central European Countries. Finance a úvěr. 2010, Vol. 60, No. 1, pp. 22-39.
  17. LINTON, O. B.; YAN Y. 2011. Semi- and Nonparametric ARCH processes. Journal of Probability and Statistics, Vol. 2011, Article ID 906212, 17 pages. Go to original source...
  18. MANDEL, M.; TOMŠÍK, V. 2008. Monetární ekonomie v malé otevřené ekonomice. 2. rozšířené vydání. Praha: Management Press, 2008.
  19. MARQUARDT, D. 1963. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal on Applied Mathematics. 1963, Vol. 11, No. 2, pp. 431-441. Go to original source...
  20. MISHRA, S.; SU, L.; ULLAH, A. 2010. Semiparametric Estimator of Time Series Conditional Variance. Journal of Business & Economic Statistics. 2010, Vol. 28, No. 2, pp. 256-274. Go to original source...
  21. POŠTA, V. 2012. Estimation of the Time Varying Risk Premium in the Czech Foreign Exchange Market. Prague Economic Papers. 2012, Vol. 21, No. 1, pp. 3-17. Go to original source...
  22. STORN, R.; PRICE, K. 1997. Differential Evolution - a Simple and Efficient Heuristic for Global Optimization. J. Global Optimization. 1997, Vol. 11, pp. 341-359. Go to original source...
  23. STULZ, R. 1994. International Portfolio Choice and Asset Pricing: An Integrative Survey. NBER Working paper No. 4645, NBER, Cambridge, MA. Go to original source...
  24. TVRDÍK, J. 2004. Evoluční algoritmy. Učební texty Ostravské University, Ostrava, 2004.
  25. WASSERMAN, L. 2007. All of Nonparametric Statistics. Secaucus, NJ: Springer-Verlag New York, Inc., 2007.

This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY NC ND 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.