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A local unit root test in mean for financial time series

A common financial trading strategy involves exploiting mean-reverting behaviour of paired asset prices. Since a unit root test can be used to determine which pairs of assets appear to exhibit mean-reverting behaviour, we propose a new Bayesian unit root to detect the presence of a local unit root vs. mean-reverting nonlinear smooth transition heteroskedastic alternative hypotheses. This test procedure is based on the posterior odds. For simultaneous estimation and inference, we employ an adaptive Bayesian Markov chain Monte Carlo scheme, which utilizes a mixture prior specification to solve the likelihood identification problem of the smoothing parameter and the autoregressive coefficient with a unit root. The size and power properties of the proposed method are examined via a simulation study. An empirical study examines the mean-reverting behaviour of price differential between stock and future.