Orthogonal series density estimation is a powerful nonparametric estimation methodology that allows one to analyze and present data at hand without any prior opinion about shape of an underlying density. The idea of construction of an adaptive orthogonal series density estimator is explained on the classical example of a direct sample from a univariate density. Data-driven estimators, which hav...

In this paper we calibrate the stationary Gaussian Musiela model to time series of market data using the Karhunen-Loeve expansion in order to get an ortonormal basis (classically known as EOF, empirical orthonormal functions) in a separable Hilbert space. The basis found is optimal for representing the covariance of the invariant measure of the forward rates’ process.

In this paper, time series prediction is considered as a problem of missing values. A new method for the determination of the missing time series values is presented. The new method is based on two projection methods: a nonlinear one (Self-Organized Maps) and a linear one (Empirical Orthogonal Functions). The presented global methodology combines the advantages of both methods to get accurate c...