Fractional Cointergration: Bayesian Inferences using a Jeffreys Prior

The concept of fractional cointegration, whereby deviations from an equilibrium relationship follow a fractionally integrated process, has attracted some attention of late. The extended concept allows cointegration to be associated with mean reversion in the error, rather than requiring the more stringent condition of stationarity. This paper presents a Bayesian method for conducting inference about fractional cointegration. The method is based on an approximation of the exact likelihood, with a Jeffreys prior being used to offset an identification problem. Inferences are based on marginal posterior densities, estimated via a combination of Markov chain Monte Carlo algorithms. The procedure is applied to several purchasing power parity relations, with substantial evidence found in favor of parity reversion.