Bayesian unit root test in nonnormal AR(1) model (Q2703260)

An AR(1) model with constant term is considered: \(y_t-\mu=\rho(y_{t-1}-\mu)+u_t\), where \(u_t\) are i.i.d. with Edgeworth series distribution with finite first four cumulants and negligible higher order cumulants. The hypothesis \(H_0:\rho=1\) is tested against \(H_1:\rho\in(a,1]\) with uniform prior on \((a,1]\), normal prior for \(\mu\) and uniform (non-informative) priors for the cumulants \(\kappa_3\) and \(\kappa_4\).NEWLINENEWLINENEWLINEThe authors derive the posterior odds ratio for the Bayesian test in this case. The results are applied to data on the currency exchange rates for 8 countries at the period 1973-1995. It is demonstrated (by the Jarque-Bera test) that the distributions of disturbances are nonnormal in this data. As a result, a case was found where \(H_0\) can be rejected by the Dickey-Fuller test but not by the Bayesian analysis.