A Diagnostic Test for Nonlinear Serial Dependence in Time Series Fitting Errors

Abstract.Time series analysts have begun to consider the applicability of nonlinear models. In order for nonlinear models to be accepted by practitioners, practicai tests must be avilable to test for the presence of nonlinearity in both raw time series and in the residuals from fitted models. A diagnostic test, based on the bispectrum, for the presence of nonlinear serial dependence in these time series is investigated here using artificial data. Detection of such nonlinear dependence is taken to indicate that nonlinear modelling methods are necessary. The theory behind the test is reviewed and simulations driven by pseudorandom numbers are presented for a variety of models and sample sizes. The simulations indicate that the test has substantial power for many models. In addition, theoretical and empirical results are presented which show that the bispectral diagnostic test is equally powerful for both the source series and for the fitting errors from a line& model. Thus, while the test is suitable for use as a diagnostic test on the fitting errors of linear time series models, prior linear modeling of the time series is not required.