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Computing and estimating information matrices of weak arma models

  • Boubacar Mainassara, Yacouba
  • Carbon, Michel
  • Francq, Christian

Numerous time series admit "weak" autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher information matrices. We give analytic expressions and propose consistent estimators of these matrices, at any point of the parameter space. Our results are illustrated by means of Monte Carlo experiments and by analyzing the dynamics of daily returns and squared daily returns of financial series.

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File URL: https://mpra.ub.uni-muenchen.de/27685/1/MPRA_paper_27685.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 27685.

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Date of creation: 2010
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Handle: RePEc:pra:mprapa:27685
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  1. Francq, Christian & Zakoïan, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 114-144, January.
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  3. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  4. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
  5. Mak, T. K. & Wong, H. & Li, W. K., 1997. "Estimation of nonlinear time series with conditional heteroscedastic variances by iteratively weighted least squares," Computational Statistics & Data Analysis, Elsevier, vol. 24(2), pages 169-178, April.
  6. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  7. Christian Francq & Jean-Michel Zako�An, 2006. "Linear-representation Based Estimation of Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 785-806.
  8. Francq, Christian & ZakoI¨an, Jean-Michel, 2008. "Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3027-3046, February.
  9. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier.
  10. André Klein & Guy Melard, 1990. "Fisher's information matrix for seasonal autoregressive-moving average models," ULB Institutional Repository 2013/13718, ULB -- Universite Libre de Bruxelles.
  11. André Klein & Guy Melard, 2004. "An algorithm for computing the asymptotic Fisher information matrix for seasonal SISO models," ULB Institutional Repository 2013/13746, ULB -- Universite Libre de Bruxelles.
  12. Christian Francq & Jean-Michel Zakoïan, 2009. "Bartlett's formula for a general class of nonlinear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 449-465, 07.
  13. Christian Francq & Jean-Michel Zakoïan, 1997. "Covariance Matrix Estimation for Estimators of Mixing Wold's Arma," Working Papers 97-19, Centre de Recherche en Economie et Statistique.
  14. Sejling, Ken & Madsen, Henrik & Holst, Jan & Holst, Ulla & Englund, Jan-Eric, 1994. "Methods for recursive robust estimation of AR parameters," Computational Statistics & Data Analysis, Elsevier, vol. 17(5), pages 509-536, June.
  15. Das, Sonjoy & Spall, James C. & Ghanem, Roger, 2010. "Efficient Monte Carlo computation of Fisher information matrix using prior information," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 272-289, February.
  16. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
  17. Christian Francq & Jean-Michel Zakoïan, 1997. "Estimating Weak Garch Representations," Working Papers 97-40, Centre de Recherche en Economie et Statistique.
  18. E. J. Godolphin & S. R. Bane, 2006. "On the Evaluation of the Information Matrix for Multiplicative Seasonal Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 167-190, 03.
  19. André Klein & Guy Mélard, 2004. "An algorithm for computing the asymptotic fisher information matrix for seasonal SISO models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 627-648, 09.
  20. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
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