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Kernel Autocorrelogram for Time Deformed Processes


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  • Eric Ghysels


  • Christian Gouriéroux
  • Joanna Jasiak


The purpose of the paper is to propose an autocorrelogram estimation procedure for irregularly spaced data which are modelled as subordinated continuous time series processes. Such processes, also called time deformed stochastic processes, have been discussed in a variety of contexts. Before entertaining the possibility of modelling such time series one is interested in examining simple diagnostics and data summaries. With continuous time processes this is a challenging task which can be accomplished via kernel estimation. This paper develops the conceptual framework, the estimation procedure and its asymptotic properties. An illustrative empirical example is also provided. L'objectif de cet article est de proposer une procédure d'estimation des autocorrélations pour les processus échantillonnés à des intervalles inégaux, modélisés comme processus subordonnés en temps continu. Ces processus, que l'on appelle aussi processus avec déformation du temps, ont été proposés dans plusieurs contextes. Avant d'élaborer sur la possibilité de modélisation des séries temporelles de ce type, on s'intéresse tout d'abord au diagnostic et à l'analyse des statistiques descriptives. Dans le domaine des processus en temps continu, cette difficile tâche peut être accomplie en ayant recours à la méthode d'estimation de l'autocorrélation par noyau. Cet article présente le cadre conceptuel, la procédure d'estimation et ses propriétés asymptotiques. Pour illustrer, un exemple empirique est aussi inclus.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 96s-19.

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Date of creation: 01 Jul 1996
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Handle: RePEc:cir:cirwor:96s-19

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Keywords: Subordinated Processes; Irregularly Spaced Data; Continuous Time Processes; Nonparametric Methods; Processus subordonnés; Observations manquantes; Processus en temps continu; Méthodes non paramétriques;

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  1. Hardle, W., 1992. "Applied Nonparametric Methods," Papers, Tilburg - Center for Economic Research 9206, Tilburg - Center for Economic Research.
  2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers, Toulouse - GREMAQ 95.400, Toulouse - GREMAQ.
  3. Florens, Jean-Pierre & Mouchart, Michel, 1985. "A Linear Theory for Noncausality," Econometrica, Econometric Society, Econometric Society, vol. 53(1), pages 157-75, January.
  4. Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
  5. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  6. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: an Application of trading Volume and Leverage Effects," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9403, Universite de Montreal, Departement de sciences economiques.
  7. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  8. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  9. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
  10. HÄRDLE, Wolfgang & VIEU, Philippe, . "Kernel regression smoothing of time series," CORE Discussion Papers RP -981, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
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Cited by:
  1. Christian Gourieroux & Gaëlle Le Fol, 1997. "Volatilités et mesures de risque," Post-Print halshs-00877048, HAL.


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