Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models
研究发现指数平滑转换自回归（ESTAR）模型中的指数函数作为区制权重函数存在两个缺陷：小参数时近似二次函数导致识别问题，大参数时类似指示函数导致过度拟合，从而引发估计困难。
Abstract Exponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill‐suited as a regime weighting function because of two undesirable properties. Firstly, 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 an identification problem with respect to the transition function parameter and the slope vector, as both enter as a product into the conditional mean of the model. Secondly, the exponential regime weighting function can behave like an indicator function (or dummy variable) for very large values of γ . This has the effect of ‘spuriously overfitting’ a small number of observations around the location parameter μ . We show that both of these effects lead to estimation problems in ESTAR models. We illustrate this by means of an empirical replication of a widely cited study, as well as a simulation exercise.