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A flexible approach to parametric inference in nonlinear time series models

Koop, G.M. and Potter, S. (2005) A flexible approach to parametric inference in nonlinear time series models. Working paper. University of Strathclyde. (Unpublished)

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Abstract

Many structural break and regime-switching models have been used with macroeconomic and �nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speci�cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. 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 everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually 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, drawing on the existing literature. We use arti�cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth.