Evaluating the Effectiveness of State-switching Time Series Models for U.s. Real Output

Two types of state-switching models for U.S. real output have been proposed: models that switch randomly between states (as in Hamilton (1989)) and models that switch states deterministically, as in the threshold autoregressive model of Potter (1995). These models have been justified primarily on how well they fit the sample data, yielding statistically significant estimates of the model coefficients. Here we apply a new method for evaluating nonlinear time series models which complements existing methods based on in-sample fit and on out-of-sample forecasting. In this new approach a battery of distinct nonlinearity tests is applied to the sample data, resulting in a set of p-values for rejecting the null hypothesis of a linear generating mechanism. This set of p-values is taken to be a “stylized fact” characterizing the nonlinearity in the generating mechanism of the time series. The effectiveness of a particular estimated model for this time series is then quantified in terms of the congruence of simulated data from this model with this stylized fact; this new approach yields a statistical test of the hypothesis that the actual sample data were generated by the estimated process. Applying the method to several state-switching models of U.S. real output – two that switch randomly and two that switch deterministically – we find that none can adequately account for the nonlinear serial dependence in this time series. JEL classification: E32, C22, C40