Diagnostic checking in a flexible nonlinear time series model

This paper considers a sequence of misspecification tests for a flexible nonlinear time series model. The model is a generalization of both the smooth transition autoregressive (STAR) and the autoregressive artificial neural network (AR-ANN) models. The tests are Lagrange multiplier (LM) type tests of parameter constancy against the alternative of smoothly changing ones, of serial independence, and of constant variance of the error term against the hypothesis that the variance changes smoothly between regimes. The small sample behaviour of the proposed tests is evaluated by a Monte-Carlo study and the results show that the tests have size close to the nominal one and a good power.