Computing and estimating information matrices of weak arma models
AbstractNumerous 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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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 27685.
Date of creation: 2010
Date of revision:
Asymptotic relative efficiency (ARE); Bahadur's slope; Information matrices; Lagrange Multiplier test; Nonlinear processes; Wald test; Weak ARMA models;
Other versions of this item:
- Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-03 (All new papers)
- NEP-ECM-2011-01-03 (Econometrics)
- NEP-ETS-2011-01-03 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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97-40, Centre de Recherche en Economie et Statistique.
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Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
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- 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.
- 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.
- 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.
- 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.
- Christian Francq & Jean-Michel Zakoïan, 2011. "Estimating the Marginal Law of a Time Series with Applications to Heavy Tailed Distributions," Working Papers 2011-30, Centre de Recherche en Economie et Statistique.
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