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Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation

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  • Lumsdaine, Robin L

Abstract

This paper compares GARCH(1,1) and IGARCH(1,1) models via a Monte Carlo study of the finite sample properties of the maximum likelihood estimator and related test statistics. While the asymptotic distribution is well approximated by the estimated t statistics, other commonly used statistics do not behave as well. In addition, the estimators themselves are skewed in small samples. For the null hypothesis of IGARCH(1,1), Wald tests typically have the best size while the standard Lagrange multiplier statistic is badly oversized; versions that are robust to possible nonnormality of the data perform marginally better. An empirical example demonstrates these results.

Suggested Citation

  • Lumsdaine, Robin L, 1995. "Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 1-10, January.
  • Handle: RePEc:bes:jnlbes:v:13:y:1995:i:1:p:1-10
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    Cited by:

    1. Manabu Asai & Michael McAleer, 2009. "Dynamic Conditional Correlations for Asymmetric Processes," CIRJE F-Series CIRJE-F-657, CIRJE, Faculty of Economics, University of Tokyo.
    2. Christiansen, Charlotte, 2002. "Credit spreads and the term structure of interest rates," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 279-295.
    3. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    4. Xu, Xinzhong & Taylor, Stephen J., 1995. "Conditional volatility and the informational efficiency of the PHLX currency options market," Journal of Banking & Finance, Elsevier, vol. 19(5), pages 803-821, August.
    5. Marcel P. Visser, 2011. "GARCH Parameter Estimation Using High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 162-197, Winter.
    6. Teruo Nakatsuma & Hiroki Tsurumi, 1996. "ARMA-GARCH Models: Bayes Estimation Versus MLE, and Bayes Non-stationarity Test," Departmental Working Papers 199619, Rutgers University, Department of Economics.
    7. Stelios Arvanitis & Antonis Demos, "undated". "A Class of Indirect Inference Estimators: Higher Order Asymptotics and Approximate Bias Correction (Revised)," DEOS Working Papers 1411, Athens University of Economics and Business, revised 23 Sep 2014.
    8. Denise R. Osborn & Christos S. Savva & Len Gill, 2008. "Periodic Dynamic Conditional Correlations between Stock Markets in Europe and the US," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 307-325, Summer.
    9. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    10. Martens, Martin, 2001. "Forecasting daily exchange rate volatility using intraday returns," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 1-23, February.
    11. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    12. Rodrigo Alfaro & Carmen Gloria Silva, 2008. "Measuring Equity Volatility: the case of Chilean Stock Index," Working Papers Central Bank of Chile 462, Central Bank of Chile.
    13. Till Strohsal & Enzo Weber, 2014. "Mean-variance cointegration and the expectations hypothesis," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1983-1997, November.
    14. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    15. Deb, Partha, 1997. "Finite sample properties of the ARCH class of models with stochastic volatility," Economics Letters, Elsevier, vol. 55(1), pages 27-34, August.
    16. Farooq Malik, 2015. "Revisiting the relationship between risk and return," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 25-40, January.
    17. Stanislav Anatolyev & Stanislav Khrapov, 2015. "Right on Target, or Is it? The Role of Distributional Shape in Variance Targeting," Econometrics, MDPI, Open Access Journal, vol. 3(3), pages 1-23, August.
    18. Benedicto Lukanima & Raymond Swaray, 2014. "Market Reforms and Commodity Price Volatility: The Case of East African Coffee Market," The World Economy, Wiley Blackwell, vol. 37(8), pages 1152-1185, August.
    19. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(2), pages 95-116, June.

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