Unit Roots: Bayesian Significance Test

Abstract

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.

Cointegration and Unit Root Tests: A Fully Bayesian Approach

“…Another alternative is to use approximation techniques, such as those proposed in [ 15 ], based on a Laplace approximation. We discuss how to implement such approximations for unit root and cointegration tests in [ 3 , 4 ].…”

“…More specifically, we will compare its performance with the most used frequentist alternatives, the ADF for unit roots, and the maximum eigenvalue test for cointegration. Since this is a review article, it is important to remark that the results presented here were published elsewhere by the same authors, see [ 3 , 4 ].…”

A Bayesian binary algorithm for root mean squared-based acoustic signal segmentation

“…However, in [21], an evidence measure for sharp hypothesis is presented; this measure is shown to be fully Bayesian (in the sense that it arrives directly from a particular cost function [18]), and to possess many desirable properties. The literature presents already many situations where this measure was succesfully applied [6,4,2,7] to sharp hypothesis settings in different problems.…”

Optimization Models for Reaction Networks: Information Divergence, Quadratic Programming and Kirchhoff’s Laws

“…The logical and operational properties of the FBST differ significantly from the well-known Bayes Factors, the standard Bayesian choice for accessing non-sharp hypotheses. However, the FBST approach can easily handle important sharp hypotheses problems using a direct approach and standard priors, while Bayes Factors require convoluted constructions, see [3,4].…”