Price convergence: Representation and testing

This paper provides a new, unified, and flexible framework to measure and characterize a convergence process in time series. We formally define a general notion of price convergence, which encompasses convergence as steady-state and catching-up, and propose a model to represent a wide range of transition paths. Our framework enables the measurement of such transitional behaviors and the development of testing procedures. In particular, we use existing unit root tests (with and without breaks) to determine whether asymptotic convergence exists and, if so, its starting point and type: as steady-state or catching-up and in its weak or strong version. We illustrate the power and flexibility of the methodology with two different datasets with potential convergence processes: (1) the aggregated price level of the Eurozone's largest economies (Germany, France and Italy) after the introduction of the common currency and, (2) the transatlantic 19th Century wheat prices.