The paper presents the three different stochastic unit root models (STUR), proposed by Granger and Swanson (1997), by Leybourne, McCabe and Mills (1996) and finally by Francq, Makarova, Zakoian (2008). The main purpose is to develop an MCMC algorithm for Bayesian estimation. We are also interested how the different specifications of the stochastic unit root affect the explanatory power of a set of competing models. We apply that these computational methods to daily exchange rates of foreign currencies in zlotys, namely Swiss franc, Pound sterling and Euro. The model selection and posterior estimates provide strong evidence in favor of the STUR models.
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