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Nonparametric Modeling in Financial Time Series

In: Handbook of Financial Time Series

Author

Listed:
  • Jürgen Franke

    (Universität Kaiserslautern, Department of Mathematics)

  • Jens-Peter Kreiss

    (Technische Universität Braunschweig, Institut für Mathematische Stochastik)

  • Enno Mammen

    (Universität Mannheim, Abteilung Volkswirtschaftslehre)

Abstract

In this chapter, we deal with nonparametric methods for discretely observed financial data. The main ideas of nonparametric kernel smoothing are explained in the rather simple situation of density estimation and regression. For financial data, a rather relevant topic is nonparametric estimation of a volatility function in a continuous-time model such as a homogeneous diffusion model. We review results on nonparametric estimation for discretely observed processes, sampled at high or at low frequency. We also discuss application of nonparametric methods to testing, especially model validation and goodness-of-fit testing. In risk measurement for financial time series, conditional quantiles play an important role and nonparametric methods have been successfully applied in this field too. At the end of the chapter we discuss Grenander’s sieve methods and other more recent advanced nonparametric approaches.

Suggested Citation

  • Jürgen Franke & Jens-Peter Kreiss & Enno Mammen, 2009. "Nonparametric Modeling in Financial Time Series," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 40, pages 927-952, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-71297-8_40
    DOI: 10.1007/978-3-540-71297-8_40
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