Previous studies investigating threshold behavior in real-exchange-rate and price difference data have used rather ad hoc statistical methods and have focused on univariate threshold models for relative prices. We utilize a general multivariate threshold cointegration model and develop a systematic testing and estimation strategy for this model, building on the work of others. Using Monte Carlo experiments, we systematically compare the use of univariate and multivariate techniques for testing threshold cointegration, estimating various threshold models, and testing specifications. We apply our methodology to a large set of U.S. disaggregated CPI data. We find evidence of threshold cointegration mainly for tradable goods. However, the type of threshold nonlinearity that we find generally does not support the transaction-cost view of commodity arbitrage.