Showing papers by "Jens Perch Nielsen published in 1996"

An Optimization Interpretation of Integration and Backfitting Estimators for Separable Nonparametric Models

Abstract: We provide an optimization interpretation of both back‐fitting and integration estimators for additive nonparametric regression. We find that the integration estimator is a projection with respect to a product measure. We also provide further understanding of the back‐fitting method. (This abstract was borrowed from another version of this item.)

Nonparametric Autoregression with Multiplicative Volatility and Additive Mean

Abstract: For over a decade, nonparametric modelling has been successfully applied to study nonlinear structures in financial time series. It is well known that the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag. When the mean has an additive structure, however, better estimation methods are available which fully exploit such a structure. Although in the past such nonparametric applications had been focused more on the estimation of the conditional mean, it is equally if not more important to measure the future risk of the series along with the mean. For the volatility function, i.e., the conditional variance given the past, a multiplicative structure is more appropriate than an additive one, as the volatility is a positive scale function and a multiplicative model provides a better interpretation of each lagged value's influence on such a function. In this paper we consider the joint estimation of both the additive mean and the multiplicative volatility. The technique used is marginally integrated local polynomial estimation. The procedure is applied to the DEM/USD (Deutsche Mark/US Dollar) daily exchange returns.