The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test.

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule ( 1926 Yule , G. U. ( 1926 ). Why we do sometimes get nonsense-correlations between time-series? A study in sampling and the nature of time-series (with discussion) . J. Roy. Statist. Soc. 89 : 1 – 64 . [Crossref] [Google Scholar] ). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. ( 1999 Bauwens , L. , Lubrano , M. , Richard , J.-F. ( 1999 ). Bayesian Inference in Dynamic Econometric Models . Oxford : Oxford University Press . [Google Scholar] ) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. The present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used.

We propose two Bayesian multinomial-Dirichlet models to predict the final outcome of football (soccer) matches and compare them to three well-known models regarding their predictive power. All the models predicted the full-time results of 1710 matches of the first division of the Brazilian football championship and the comparison used three proper scoring rules, the proportion of errors and a calibration assessment. We also provide a goodness of fit measure. Our results show that multinomial-Dirichlet models are not only competitive with standard approaches, but they are also well calibrated and present reasonable goodness of fit.

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 Full 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.

The 37th edition of MaxEnt was held in Brazil, hosting several distinguished researchers and students. The workshop offered four tutorials, nine invited talks, twenty four oral presentations and twenty seven poster presentations. All submissions received their first choice between oral and poster presentations. The event held a celebration to Julio Stern’s 60th anniversary and awarded two prizes to young researchers. As customary, the workshop had one free afternoon, in which participants visited the city’s surroundings and experienced Brazilian food and traditions.