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Nonlinear Autocorrelograms: an Application to Inter‐Trade Durations

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  • CHRISTIAN GOURIÉROUX
  • JOANN JASIAK

Abstract

The paper presents a study of temporal dependence in nonlinear transformations of time series. We examine the effects of parametric transformations on autocorrelation values and the persistence range with special emphasis on long memory processes. We derive an invariance property for the order of fractional integration of transformed normal processes and propose a related specification test. Within the class of nonlinear time series transforms, we identify those which maximize autocorrelations at selected lags. This procedure is based on nonlinear canonical correlations analysis adapted to serially correlated data. The methods proposed in this paper may be applied to various financial time series that usually are transformed prior to estimation, like returns, volumes or inter‐trade durations. In examples illustrating our approach, we use series of durations between trades of the Alcatel stock on the Paris Bourse.

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  • Christian Gouriéroux & Joann Jasiak, 2002. "Nonlinear Autocorrelograms: an Application to Inter‐Trade Durations," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(2), pages 127-154, March.
    • Handle: RePEc:bla:jtsera:v:23:y:2002:i:2:p:127-154
    DOI: 10.1111/1467-9892.00259
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    Cited by:

    1. Christian Gourieroux & Joann Jasiak, 2011. "Nonlinear Persistence and Copersistence," Palgrave Macmillan Books, in: Greg N. Gregoriou & Razvan Pascalau (ed.), Nonlinear Financial Econometrics: Markov Switching Models, Persistence and Nonlinear Cointegration, chapter 4, pages 77-103, Palgrave Macmillan.
    2. Vladimir Filimonov & Didier Sornette, 2013. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Papers 1308.6756, arXiv.org, revised Jul 2014.
    3. Drost, Feike C & Werker, Bas J M, 2004. "Semiparametric Duration Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 40-50, January.
    4. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    5. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.
    6. J. V. Andersen & D Sornette, 2003. "Fearless versus Fearful Speculative Financial Bubbles," Papers cond-mat/0311089, arXiv.org.

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