Nonparametric Models

Abstract

Parametric time series models provide powerful tools for analyzing time series data when the models are correctly specified. However, any parametric models are at best only an approximation to the true stochastic dynamics that generates a given data set. The issue of modeling biases always arises in parametric modeling. One conventional technique is to expand the parametric models from a smaller family to a larger family. This eases the concerns on modeling biases but is not necessarily the most effective way to deal with them. As mentioned in §1.3.3, a good fitting for a simple MA series by an AR model may require a high order. Similarly, a simple nonlinear series might require a high order of ARMA model to reasonably approximate it. Thus, the choice for the form of a parametric model is very critical.