Bayesian Arbitrage Threshold Analysis

A Bayesian estimation procedure is developed for estimating multiple regime (multiple threshold) vector autoregressive models appropriate for deviations from financial arbitrage relationships. This approach has clear advantages over classical stepwise threshold autoregressive analysis. Whereas classical procedures first have to identify thresholds and then perform piecewise autoregressions, we simultaneously estimate threshold and autoregression parameters. To illustrate the Bayesian procedure, we estimate a no-arbitrage band within which index futures arbitrage is not profitable despite (persistent) deviations from parity.