Estimating the Marginal Law of a Time Series with Applications to Heavy Tailed Distributions
AbstractThis article addresses estimating parametric marginal densities of stationary time series in the absence of precise information on the dynamics of the underlying process. We propose using an estimator obtained by maximization of the "quasi-marginal" likelihood, which is a likelihood written as if the observations were independent. We study the effect of the (neglected) dynamics on the asymptotic behavior of this estimator. The consistency and asymptotic normality of the estimator are established under mild assumptions on the dependence structure. Applications of the asymptotic results to the estimation of stable, generalized extreme value and generalized Pareto distributions are proposed. The theoretical results are illustrated on financial index returns. Supplementary materials for this article are available online.
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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2011-30.
Date of creation: 2011
Date of revision:
alpha-stable distribution; composite likelihood; GEV distribution; GPD; pseudo-likelihood; quasi-marginal maximum likelihood; stock returns distributions;
Other versions of this item:
- Christian Francq & Jean-Michel ZakoÃ¯an, 2013. "Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 412-425, October.
- NEP-ALL-2012-05-22 (All new papers)
- NEP-ECM-2012-05-22 (Econometrics)
- NEP-ETS-2012-05-22 (Econometric Time Series)
- NEP-RMG-2012-05-22 (Risk Management)
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.:
- Shiqing Ling & Michael McAleer, 2010.
"A general asymptotic theory for time-series models,"
Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 97-111.
- Shiqing Ling & Michael McAleer, 2009. "A General Asymptotic Theory for Time Series Models," CIRJE F-Series CIRJE-F-670, CIRJE, Faculty of Economics, University of Tokyo.
- Cotter, John, 2007.
"Varying the VaR for unconditional and conditional environments,"
Journal of International Money and Finance,
Elsevier, vol. 26(8), pages 1338-1354, December.
- John Cotter, 2011. "Varying the VaR for Unconditional and Conditional Environments," Working Papers 200419, Geary Institute, University College Dublin.
- John Cotter, 2011. "Varying the VaR for Unconditional and Conditional Environments," Papers 1103.5649, arXiv.org.
- Cotter, John, 2004. "Varying the VaR for Unconditional and Conditional Environments," MPRA Paper 3483, University Library of Munich, Germany.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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.
- 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.
- Boubacar Mainassara, Yacouba & Carbon, Michel & Francq, Christian, 2010. "Computing and estimating information matrices of weak arma models," MPRA Paper 27685, University Library of Munich, Germany.
- Dennis Jansen & Casper de Vries, 1988.
"On the frequency of large stock returns: putting booms and busts into perspective,"
1989-006, Federal Reserve Bank of St. Louis.
- Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
- Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 169-187.
- Stephen J. Taylor, 2007.
"Introduction to Asset Price Dynamics, Volatility, and Prediction
[Asset Price Dynamics, Volatility, and Prediction]," Introductory Chapters, Princeton University Press.
- Einmahl, John H. J. & Li, Jun & Liu, Regina Y., 2009. "Thresholding Events of Extreme in Simultaneous Monitoring of Multiple Risks," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 982-992.
- Auray, Stéphane & Eyquem, Aurélien & Jouneau-Sion, Frédéric, 2014.
"Modeling tails of aggregate economic processes in a stochastic growth model,"
Computational Statistics & Data Analysis,
Elsevier, vol. 76(C), pages 76-94.
- Stéphane Auray & Aurélien Eyquem & Fréderic Jouneau-Sion, 2012. "Modelling Tails of Aggregated Economic Processes in a Stochastic Growth Model," Working Papers 2012-29, Centre de Recherche en Economie et Statistique.
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