Approximate Bayes factors for unit root testing

TL;DR

This paper presents a practical Bayesian approach for unit root testing in financial time series, using an approximation of the Bayes factor based on BIC, which is easy to implement and effective.

Contribution

It introduces a new approximation method for Bayes factors in unit root testing that is simple, assumption-light, and does not require prior distributions.

Findings

The method aligns well with Bayesian and non-Bayesian tests.

It maintains a good error rate across simulations.

Empirical results on exchange rates validate its effectiveness.

Abstract

This paper introduces a feasible and practical Bayesian method for unit root testing in financial time series. We propose a convenient approximation of the Bayes factor in terms of the Bayesian Information Criterion as a straightforward and effective strategy for testing the unit root hypothesis. Our approximate approach relies on few assumptions, is of general applicability, and preserves a satisfactory error rate. Among its advantages, it does not require the prior distribution on model's parameters to be specified. Our simulation study and empirical application on real exchange rates show great accordance between the suggested simple approach and both Bayesian and non-Bayesian alternatives.