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Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models

44 Pages Posted: 13 Apr 2016 Last revised: 16 Sep 2017

Daniel Buncic

Sveriges Riksbank

Date Written: September 15, 2017


Exponential smooth transition autoregressive (ESTAR) models have been widely used in the empirical international finance literature. We show that the exponential function used in ESTAR models is ill-suited as a regime weighting function because of two undesirable properties. The first is that it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter γ, which governs the shape of the function, is ‘small’. This leads to identification issues with respect to the transition function parameter and the slope vector in ESTAR models. The second is that the exponential function becomes an indicator function over the entire range of the threshold variable, except at the point where the threshold variable is equal to the location parameter µ. This results in a high propensity to spuriously overfit a small number of observations around µ, leading to an ‘outlier fitting effect’ of the exponential function. We show the effect of both of these problems on estimation of ESTAR models by means of an empirical replication of the well known study by Taylor et al. (2001), and an extensive simulation exercise, where we vary the magnitude of the threshold parameter as well as the sample size.

Keywords: Exponential STAR, non-linear time series models, identification and estimation issues, exponential weighting function, real exchange rates, simulation analysis

JEL Classification: C13, C15, C50, F30, F44

Suggested Citation

Buncic, Daniel, Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models (September 15, 2017). Available at SSRN:

Daniel Buncic (Contact Author)

Sveriges Riksbank ( email )

Brunkebergstorg 11
SE-103 37 Stockholm

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