Cointegration and unit root tests: A fully Bayesian approach

TL;DR

This paper reviews Bayesian methods for testing unit roots and cointegration in time series, highlighting the advantages of the fully Bayesian significance test over traditional frequentist approaches.

Contribution

It demonstrates how the fully Bayesian significance test can address shortcomings of existing Bayesian and frequentist tests for unit roots and cointegration.

Findings

FBST outperforms traditional tests in certain scenarios.

Comparison shows improved accuracy of Bayesian approach.

Provides a comprehensive review of Bayesian time series testing methods.

Abstract

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.