Testing for Neglected Nonlinearity Using Regularized Articial Neural Networks
The Artificial Neural Network (ANN) test of Lee, White and Granger (LWG, 1993) uses the ability of the ANN activation functions in the hidden layer to detect neglected functional misspecification. As the estimation of the ANN model is often quite difficult, LWG suggested activate the ANN hidden units based on randomly drawn activation parameters. To be robust to the random activations, a large number of activations are desirable. This leads to a situation for which regularization of the dimensionality is needed by techniques such as Principal Component Analysis (PCA), Lasso, Pretest, Partial Least Squares (PLS), among others.