The Additive Random Field Regression Model∗

We study additive models within the context of the parametric random field model proposed by Hamilton (2001). This is a flexible parametric approach to model nonlinearities in the context of a regression model. Though the model is parametric, it enjoys the flexibility of the nonparametric approach as it can approximate a large collection of nonlinear functions and it has the added advantage that there is no “curse of dimensionality”. If the true data generating process is additive, we propose a new specification of the random field model that is shown to have more accurate out of sample predictions than the Hamilton’s model. For a fixed sample and for k regressors, we approximate the individual contribution of each regressor to the conditional mean by a random field, such that the nonlinear part is the sum of k individual and independent random fields as opposed to the Hamilton’s model where one random field approximates the joint contribution of the k regressors. We ∗The notation follows Abadir and Magnus (2002). †Corresponding author.