ABSTRACT
Non-parametric methods are widely used in non-linear model building. Such methods are particularly useful if no prior information about the structure is available, since the estimation procedure is free of parameters and model structure. This chapter describes some statistical methods for identification of discrete and continuous-time models of interest rates, foreign exchange rates, stock prices and other financial time series. It considers kernel estimation in general and its use in time series analysis. From kernel estimates of probability density functions, Gaussianity can be verified or the nature of non-Gaussianity can be discovered. The chapter discusses central limit theorems and applications of kernel estimators. Non-parametric methods can be applied to identify the structure of the existing relationships leading to proposals for parametric model classes. An example of identifying the diurnal dependence in a non-stationary time series is given.
