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

摘要

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. The purpose of this paper is to suggest a method for identification of the structure of linear and non-linear time series through nonparametric estimation of the unknown curves in models of the type Y_t = E(Y_t|X_t = x_t) + ε_t, where X_t = (Y_(t-1), Y_(t-2), ... , Y_(t-d)). In this paper we compare the proposed approach to others traditionally described in the literature. The series used in the numerical implementations of this study were generated from two types of model: a linear AR(2) and a non-linear ARNL(1). Each time series has 100 observations.