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Nonparametric Modeling in Financial Time Series

  • Jürgen FrankeEmail author
  • Jens-Peter Kreiss
  • Enno Mammen
Chapter

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.

Keywords

Regression Quantile Nonparametric Estimation Stochastic Volatility Nonparametric Regression Nonparametric Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jürgen Franke
    • 1
    Email author
  • Jens-Peter Kreiss
    • 2
  • Enno Mammen
    • 3
  1. 1.Department of MathematicsUniversität KaiserslauternErwin–Schrödinger-StrasseGermany
  2. 2.Institut für Mathematische StochastikTechnische Universität BraunschweigBraunschweigGermany
  3. 3.Abteilung VolkswirtschaftslehreUniversität MannheimMannheimGermany

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