Nonparametric Modeling in Financial Time Series

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 regres- sion. For financial data, a rather relevant topic is nonparametric estimation of a volatility function in a continuous-time model such as a homogeneous dif- fusion 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 riskmeasurement for financial time series, con- ditional 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.