Inference in conditional vector error correction models with a small signal-to-noise ratio

It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having cointegrated errors that are characterized simultaneously by high persistence (near-unit root behavior) and very small (near zero) variance. The proposed dual parameterization induces the cointegration error process to be stochastically bounded which prevents the variables in the cointegrating system from drifting apart over a reasonably long horizon. More specifically, this chapter develops the appropriate asymptotic theory (rate of convergence and asymptotic distribution) for the estimators in unconditional and conditional vector error correction models (VECM) when the error correction term is parameterized as a dampened near-unit root process (local-to-unity process with local-to-zero variance). The important differences in the limiting behavior of the estimators and their implications for empirical analysis are discussed. Simulation results and an empirical analysis of the forward premium regressions are also provided.