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The rate of consistency of the quasi-maximum likelihood estimator

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  • Berkes, István
  • Horváth, Lajos

Abstract

We connect the rate of consistency of the quasi-maximum likelihood estimator in GARCH(p,q) sequences with the number of the moments of the innovations.

Suggested Citation

  • Berkes, István & Horváth, Lajos, 2003. "The rate of consistency of the quasi-maximum likelihood estimator," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 133-143, January.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:2:p:133-143
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    1. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    2. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    3. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    Cited by:

    1. Gian Piero Aielli & Massimiliano Caporin, 2015. "Dynamic Principal Components: a New Class of Multivariate GARCH Models," "Marco Fanno" Working Papers 0193, Dipartimento di Scienze Economiche "Marco Fanno".
    2. Rasmus Søndergaard Pedersen & Anders Rahbek, 2015. "Nonstationary ARCH and GARCH with t-Distributed Innovations," Discussion Papers 15-07, University of Copenhagen. Department of Economics.
    3. Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2016. "Nonstationary GARCH with t-distributed innovations," Economics Letters, Elsevier, vol. 138(C), pages 19-21.
    4. repec:bgu:wpaper:0607 is not listed on IDEAS
    5. Lopes, Sílvia R.C. & Prass, Taiane S., 2014. "Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 278-307.
    6. Maia, Gisele de Oliveira & Barreto-Souza, Wagner & Bastos, Fernando de Souza & Ombao, Hernando, 2021. "Semiparametric time series models driven by latent factor," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1463-1479.
    7. Neifar, Malika, 2020. "Multivariate GARCH Approaches: case of major sectorial Tunisian stock markets," MPRA Paper 99658, University Library of Munich, Germany.
    8. PREMINGER, Arie & STORTI, Giuseppe, 2006. "A GARCH (1,1) estimator with (almost) no moment conditions on the error term," LIDAM Discussion Papers CORE 2006068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.
    10. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1265-1284, September.
    11. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    12. Berkes, Istvan & Horváth, Lajos & Kokoszka, Piotr, 2004. "Testing for parameter constancy in GARCH(p,q) models," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 263-273, December.
    13. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    14. Taewook Lee & Sangyeol Lee, 2009. "Normal Mixture Quasi‐maximum Likelihood Estimator for GARCH Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 157-170, March.

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