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)
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