A flexible approach to parametric inference in nonlinear time series models

Many structural break and regime-switching models have been used with macroeconomic and financial data. In this paper, we develop an extremely flexible parametric model that accommodates virtually any of these specifications—and does so in a simple way that allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in different ways, we can accommodate a wide range of nonlinear time series models. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for models that exhibit abrupt change as well as those that permit a gradual evolution of parameters. We show how our model will (approximately) nest almost every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward and draw on the existing literature. We use artificial data to show the advantages of our approach and then provide two empirical illustrations involving the modeling of real GDP growth.