Some New Results for Threshold AR(1) Models
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The purpose of this paper is to derive some new results for threshold models. We consider AR(1) threshold models, with either self-exciting or exogenous triggers. In the latter case, we derive necessary and sufficient conditions for the existence of a stationary distribution, which are wider than the sufficient conditions that are the consequence of theorems provided in the literature by previous authors. We note that there appear to be no results in the literature for closed-form expressions for steady-state distributions for threshold models under econometrically relevant conditions. We provide such a result for the case of a threshold AR(1) with an exogenous trigger variable and normal innovations. It turns out to be a known distribution, namely, a compound geometric sum of normals.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
