Testing for Neglected Nonlinearity in Time Series Models: A Comparison of Neural Network Methods and Alternative Tests

In this paper a new test, the neural network test for neglected nonlinearity, is compared with the Keenan test, the Tsay test, the White dynamic information matrix test, the McLeod–Li test, the Ramsey RESET test, the Brock–Dechert–Scheinkman test, and the Bispectrum test. The neural network test is based on the approximating ability of neural network modeling techniques recently developed by cognitive scientists. This test is a Lagrange multiplier test that statistically determines whether adding ‘hidden units’ to the linear network would be advantageous. The performance of the tests is compared using a variety of non-linear artificial series including bilinear, threshold autoregressive, and nonlinear moving average models, and the tests are applied to actual economic time series. The relative performance of the neural network test is encouraging. Our results suggest that it can play a valuable role in evaluating model adequacy. The neural network test has proper size and good power, and many of the economic series tested exhibit potential nonlinearities.