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Financial Point Processes

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Econometrics of Financial High-Frequency Data

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Abstract

This chapter provides the methodological background for the specification and estimation of financial point processes. We give a brief introduction to the fundamental statistical concepts and the basic ways to model point processes. For ease of introduction, we restrict our attention to non-dynamic point processes. In Sect.4.1, we discuss the most important theoretical concepts in point process theory. Here, the focus lies on the idea of the intensity function as a major concept in the theory of point processes. In Sect.4.2, different ways to model point processes are discussed. Section 4.3 is concerned with the treatment of censoring mechanisms and time-varying covariates. Section 4.4 gives an outlook on different ways to dynamically extend basic point process models.

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Notes

  1. 1.

    Point processes can also evolve over space yielding the class of spatial point processes or cluster processes, see, e.g., Daley and Vere-Jones (2005).

  2. 2.

    A càdlàg (french: continue à droite, limitée à gauche) function is a function which is right-continuous with left-hand limits.

  3. 3.

    More general types of point processes not fulfilling this property are, e.g., spatial point processes or Neymann-Scott cluster processes. For more details, see, e.g., Daley and Vere-Jones (2005).

  4. 4.

    See, e.g., Kalbfleisch and Prentice (1980), Kiefer (1988) or Lancaster (1997).

  5. 5.

    See, e.g., Daley and Vere-Jones (2005), Theorem A3.4.III.

  6. 6.

    See, e.g., Karr (1991), p. 57.

  7. 7.

    See, e.g., Kalbfleisch and Prentice (1980), Cox and Oakes (1984) or the recent survey by Oakes (2001).

  8. 8.

    A well known example is the analysis of the length of unemployment spells which is studied by a wide range of theoretical and empirical papers, see e.g. Lancaster (1979), Nickell (1979), Heckmann and Singer (1984), Moffitt (1985), Honoré (1990), Meyer (1990), Han and Hausman (1990), Gritz (1993), McCall (1996) or van den Berg and van der Klaauw (2001) among many others.

  9. 9.

    For more details, see Kalbfleisch and Prentice (1980) or in the survey of Kiefer (1988).

  10. 10.

    In this case, an intercept term has to be included in 4.39 since ε i  ∗  has a nonzero mean.

  11. 11.

    Nevertheless, the efficiency of the estimator is affected by the chosen categorization.

  12. 12.

    See Kalbfleisch and Prentice (1980).

  13. 13.

    See, e.g., Horowitz and Neumann (1987, 1989), the survey by Neumann (1997), Gorgens and Horowitz (1999) or Orbe et al. (2002).

  14. 14.

    Such processes will be discussed in more details in Chap. 10.

  15. 15.

    However, note that we cannot identify whether more than one price movement occurred during the non-trading period.

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Authors and Affiliations

  1. Institute for Statistics and Econometrics School of Business and Economics, Humboldt-Universität zu Berlin, Spandauer Str. 1, 10178, Berlin, Germany

    Professor Dr. Nikolaus Hautsch

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Hautsch, N. (2012). Financial Point Processes. In: Econometrics of Financial High-Frequency Data. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21925-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-21925-2_4

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