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On The Efficiency And Consistency Of Likelihood Estimation In Multivariate Conditionally Heteroskedastic Dynamic Regression Models

  • Enrique Sentana

    ()

  • Gabriele Fiorentini

    ()

    (CEMFI, Centro de Estudios Monetarios y Financieros)

We rank the efficiency of several likelihood-based parametric and semiparametric estimators of conditional mean and variance parameters in multivariate dynamic models with i.i.d. spherical innovations, and show that Gaussian pseudo maximum likelihood estimators are inefficient except under normality. We also provide conditions for partial adaptivity of semiparametric procedures, and relate them to the consistency of distributionally misspecified maximum likelihood estimators. We propose Hausman tests that compare Gaussian pseudo maximum likelihood estimators with more efficient but less robust competitors. We also study the efficiency of sequential estimators of the shape parameters. Finally, we provide finite sample results through Monte Carlo simulations.

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Paper provided by CEMFI in its series Working Papers with number wp2007_0713.

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Date of creation: Sep 2007
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Handle: RePEc:cmf:wpaper:wp2007_0713
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  1. Douglas Hodgson, 2000. "Unconditional pseudo-maximum likelihood and adaptive estimation in the presence of conditional heterogeneity of unknown form," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 175-206.
  2. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  3. Russell Davidson & James G. MacKinnon, 1994. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," Working Papers 903, Queen's University, Department of Economics.
  4. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
  5. Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," FMG Discussion Papers dp502, Financial Markets Group.
  6. Enrique Sentana & Dante Amegual, 2008. "A Comparison Of Mean-Variance Efficiency Tests," Working Papers wp2008_0806, CEMFI.
  7. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
  8. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  9. Berkane, Maia & Bentler, P. M., 1986. "Moments of elliptically distributed random variates," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 333-335, October.
  10. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
  11. Gonzalez-Rivera, G., 1995. "A Note on Adaptation in Garch Models," The A. Gary Anderson Graduate School of Management 95-1, The A. Gary Anderson Graduate School of Management. University of California Riverside.
  12. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 251-280, April.
  13. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2004. "On the validity of the Jarque-Bera normality test in conditionally heteroskedastic dynamic regression models," Economics Letters, Elsevier, vol. 83(3), pages 307-312, June.
  14. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  15. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
  16. Sentana, E., 1994. "The Likelihood Function of a Conditionally Heteroskdastic Factor Model with Heywood Cases," Papers 9420, Centro de Estudios Monetarios Y Financieros-.
  17. N. Meddahi & C. Bontemps, 2004. "Testing Distributional Assumptions: A GMM Approach," Econometric Society 2004 North American Winter Meetings 487, Econometric Society.
  18. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 471-480, September.
  19. Hodgson, Douglas J & Vorkink, Keith P, 2003. "Efficient Estimation of Conditional Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 269-83, April.
  20. Drost, F.C. & Klaassen, C.A.J., 1996. "Efficient Estimation in Semiparametric GARCH Models," Discussion Paper 1996-38, Tilburg University, Center for Economic Research.
  21. Douglas J Hodgson & Oliver Linton & Keith Vorkink, 2000. "Testing the capital asset pricing model efficiently under elliptical symmetry : a semiparametric approach," LSE Research Online Documents on Economics 2197, London School of Economics and Political Science, LSE Library.
  22. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Wiley Blackwell, vol. 71(4), pages 945-973, October.
  23. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
  24. Oliver Linton & Douglas G. Steigerwald, 1995. "Adaptive Testing in ARCH Models," Cowles Foundation Discussion Papers 1105, Cowles Foundation for Research in Economics, Yale University.
  25. Gonzalez-Rivera, Gloria & Drost, Feike C., 1999. "Efficiency comparisons of maximum-likelihood-based estimators in GARCH models," Journal of Econometrics, Elsevier, vol. 93(1), pages 93-111, November.
  26. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
  27. Drost, F.C. & Klaassen, C.A.J., 1997. "Efficient estimation in semiparametric GARCH models," Other publications TiSEM c7de3f1c-c456-433e-a1c6-2, School of Economics and Management.
  28. Sentana, E., 2000. "Factor Representing Portfolios in Large Asset Markets," Papers 0001, Centro de Estudios Monetarios Y Financieros-.
  29. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
  30. repec:ner:tilbur:urn:nbn:nl:ui:12-74145 is not listed on IDEAS
  31. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  32. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  33. repec:ner:tilbur:urn:nbn:nl:ui:12-74146 is not listed on IDEAS
  34. Enrique SENTANA, 2000. "The Likelihood Function of Conditionally Heteroskedastic Factor Models," Annales d'Economie et de Statistique, ENSAE, issue 58, pages 1-19.
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