Identification of the Structure of Linear and Non-Linear Time Series Models, Using Nonparametric Local Linear Kernel Estimation

Abstract

The estimation procedure of a parametric linear regression model is a process of global estimation and assumes that the function E(Y t |X t ) is linear. However, in many situations, such an approach can be inadequate. On the other hand, nonparametric regression modelling allows more flexibility for the shape of the unknown function. In the nonparametric context, one possible approach is to estimate the unknown regression curve through a local polynomial kernel regression. By doing so, only points in the local neighborhood of the point X t , where E(Y t |X t =x t ) is to be estimated, will influence this estimate. In other words, with local polynomial estimators the unknown function is estimated in a way such that the observations which are near to the point where the curve is to be estimated will receive high weight, whereas those which are far will receive low weight.