A Zellner Test for Autocorrelation

In the 1960s, Arnold Zellner developed Bayesian models for first-order autoregressions. Here we extend Zellner’s parameter estimation framework and propose an associated Bayes factor test for the presence of autocorrelation. This test uses the Savage-Dickey density ratio and yields ananalytical result; moreover, the test permits a simple and accurate approximation that clarifies the relationship between the Bayes factor and p-values from the ubiquitous Ljung-Box and Wald tests. The Bayes factor test allows researchers to take into account prior knowledge, to discriminate between ‘absence of evidence’ and ‘evidence of absence’, and to monitor evidence as the data accumulate.