Computational Economics

, Volume 48, Issue 3, pp 473–485 | Cite as

On the Choice of a Genetic Algorithm for Estimating GARCH Models

  • Manuel Rizzo
  • Francesco Battaglia


The GARCH models have been found difficult to build by classical methods, and several other approaches have been proposed in literature, including metaheuristic and evolutionary ones. In the present paper we employ genetic algorithms to estimate the parameters of GARCH(1,1) models, assuming a fixed computational time (measured in number of fitness function evaluations) that is variously allocated in number of generations, number of algorithm restarts and number of chromosomes in the population, in order to gain some indications about the impact of each of these factors on the estimates. Results from this simulation study show that if the main purpose is to reach a high quality solution with no time restrictions the algorithm should not be restarted and an average population size is recommended, while if the interest is focused on driving rapidly to a satisfactory solution then for moderate population sizes it is convenient to restart the algorithm, even if this means to have a small number of generations.


Evolutionary computation Conditional heteroscedasticity Parameter estimation Restarts 



The authors wish to thank Peter Winker for useful suggestions, and an anonymous referee for valuable comments.


  1. Adanu, K. (2006). Optimizing the Garch model—An application of two global and two local search methods. Computational Economics, 28, 277–290.CrossRefGoogle Scholar
  2. Alander, J. T. (1992). On optimal population size of genetic algorithms. In Proceedings of CompEuro92 (pp. 65–70). Washington: IEEE Computer Society Press.Google Scholar
  3. Baragona, R., Battaglia, F., & Poli, I. (2011). Evolutionary statistical procedures—An evolutionary computation approach to statistical procedures design and applications. Berlin: Springer.Google Scholar
  4. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.CrossRefGoogle Scholar
  5. Bollerslev, T., & Ghysels, E. (1991). Periodic autoregressive conditional heteroskedasticity. Journal of Business & Economic Statistics, 14(2), 139–151.Google Scholar
  6. De Jong, K. A. (1975) An analysis of the behaviour of a class of genetic adaptive systems. Ph.d Thesis, Dept. of Computer and Communication Sciences University of Michigan, Ann ArborGoogle Scholar
  7. Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.CrossRefGoogle Scholar
  8. Fan, J., & Yao, Q. (2003). Nonlinear time series: Nonparametric and parametric models. New York: Springer.CrossRefGoogle Scholar
  9. Fukunaga, A. S. (1998). Restart scheduling for genetic algorithms. Lecture Notes In Computer Science, 1498, 357–366.CrossRefGoogle Scholar
  10. Geng, L., & Zhang, Z. (2015). Forecast of stock index volatility using grey garch-type models. The Open Cybernetics & Systemics Journal. doi: 10.2174/1874110X01509010093.
  11. Ghannadian, F., Alford, C., & Shonkwiler, R. (1996). Application of random restart to genetic algorithms. Intelligent Systems, 95, 81–102.Google Scholar
  12. Goldberg, D. E. (1989). Sizing populations for serial and parallel genetic algorithms. In J. D. Schafer (Ed.), Proceedings of the 3d conference of genetic algorithms (pp. 70–79). San Mateo: Morgan Kaufman.Google Scholar
  13. Grefenstette, J. J. (1992). Genetic algorithms for changing environments. In R. Manner & B. Manderick (Eds.), Parallel problem solving from nature 2 (pp. 137–144). Amsterdam: Elsevier.Google Scholar
  14. Holland, J. H. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press.Google Scholar
  15. Hung, J. (2009). A fuzzy GARCH model applied to stock market scenario using a genetic algorithm. Expert Systems with Applications, 36, 11710–11717.CrossRefGoogle Scholar
  16. Misevicius, A. (2009). Restart-based genetic algorithm for the quadratic assignment problem. In M. Bramer, F. Coenen, & M. Petridis (Eds.), Research and development in intelligent systems XXV—proceedings of AI-2008 (pp. 91–104). London: Springer.Google Scholar
  17. Phanden, R. K., Jain, A., & Verma, R. (2012). A genetic algorithm-based approach for job-shop scheduling. Journal of Manufacturing Technology Management, 23(7), 937–946.CrossRefGoogle Scholar
  18. R Core Team (2013) R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
  19. Rudolph, G. (1997). Convergence properties of evolutionary algorithms. Hamburg: Verlag Dr. Kovac.Google Scholar
  20. Santamaría-Bonfil, G., Frausto-Solís, J., Vzquez-Rodarte, I., (2015). Volatility forecasting using support vector regression and a hybrid genetic algorithm. Computational Economics. doi: 10.1007/s10614-013-9411-x.
  21. Wang, C., & Li, G. (2001). Improving the estimations of Var-GARCH using genetic algorithm. Journal of Systems Science and Systems Engineering, 10(3), 281–290.Google Scholar
  22. Winker, P. (2006). The stochastic of threshold accepting: analysis of an application to the uniform design problem. In A. Rizzi & M. Vichi (Eds.), COMPSTAT 2006—Proceeding in Computational Statistics (pp. 495–503). Heidelberg: Physica-Verlag.Google Scholar
  23. Winker, P., & Gilli, M. (2004). Applications of optimization heuristics to estimation and modelling problems. Computational Statistics & Data Analysis, 47, 211–223.CrossRefGoogle Scholar
  24. Winker, P., & Maringer, D. (2009). The convergence of estimators based on heuristics: Theory and application to a GARCH model. Computational Statistics, 24, 533–550.CrossRefGoogle Scholar
  25. Wuertz, D., et al. (2013). fGarch: Rmetrics—Autoregressive conditional heteroskedastic modelling. R package version 3010.82.
  26. Zumbach, G. (2000). The pitfalls in fitting GARCH processes. In C. Dunis (Ed.), Advances in quantitative asset management. Amsterdam: Kluver.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of StatisticsSapienza University of RomeRomaItaly

Personalised recommendations