Rank estimation in Cointegrated Vector Auto-Regression models via automated Trans-dimensional Markov chain Monte Carlo

This paper develops a novel automated Trans-dimensional Markov chain Monte Carlo sampling methodology for Bayesian Cointegrated Vector Auto Regression (CVAR) models. In automating the rank and cointegration vector estimation in CVAR models we solve an important problem in algorithmic trading of cointegrated price series. The automation of both the within model sub-space sampling for the cointegration vectors directions and the between model rank estimation Markov chain proposal is achieved by developing a global matrix-variate proposal centered on the MLE and with covariance given by the observed Fisher Information matrix. To obtain this in the matrix-variate CVAR setting under an error correction formulation (ECM) involved a non-trivial derivation of the observed Fisher information matrix for each model subspaces unconstrained cointegration vector components, conditional on the components of the long run multiplier matrix which are constrained for identifiability. We study synthetic data and futures data on U.S. treasury notes, bonds and US equity indexes. In each analysis, we compare the estimated rank based on the estimated posterior model probabilities for the rank to simple Bayes Factor estimated posterior rank probabilities and the classical hypothesis test of the rank based on the trace statistic of the long-run multiplier matrix.