  To perform statistical inference for time series, one should be able to
assess if they present deterministic or stochastic trends. For univariate
analysis one way to detect stochastic trends is to test if the series has unit
roots, and for multivariate studies it is often relevant to search for
stationary linear relationships between the series, or if they cointegrate. The
main goal of this article is to briefly review the shortcomings of unit root
and cointegration tests proposed by the Bayesian approach of statistical
inference and to show how they can be overcome by the fully Bayesian
significance test (FBST), a procedure designed to test sharp or precise
hypothesis. We will compare its performance with the most used frequentist
alternatives, namely, the Augmented Dickey-Fuller for unit roots and the
maximum eigenvalue test for cointegration. Keywords: Time series; Bayesian
inference; Hypothesis testing; Unit root; Cointegration.
