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Kernel Autocorrelogram for Time Deformed Processes

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  • Eric Ghysels
  • Christian Gouriéroux
  • Joann Jasiak

Abstract

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.

Suggested Citation

  • Eric Ghysels & Christian Gouriéroux & Joann Jasiak, 1996. "Kernel Autocorrelogram for Time Deformed Processes," CIRANO Working Papers 96s-19, CIRANO.
  • Handle: RePEc:cir:cirwor:96s-19
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    File URL: https://cirano.qc.ca/files/publications/96s-19.pdf
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    References listed on IDEAS

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    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 73-87, December.
    3. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: An Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    7. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    8. Hardle, W. & Vieu, P., 1990. "Kernel regression smoothing of time series," LIDAM Discussion Papers CORE 1990031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
    10. Florens, Jean-Pierre & Mouchart, Michel, 1985. "A Linear Theory for Noncausality," Econometrica, Econometric Society, vol. 53(1), pages 157-175, January.
    11. Wolfgang Härdle & Philippe Vieu, 1992. "Kernel Regression Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 209-232, May.
    12. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
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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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    More about this item

    Keywords

    Subordinated Processes; Irregularly Spaced Data; Continuous Time Processes; Nonparametric Methods; Processus subordonnés; Observations manquantes; Processus en temps continu; Méthodes non paramétriques;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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