Comovements between diffusion processes: Characterization, estimation, and testing

The aim of this paper is to characterize and analyze long-run comovements among diffusion processes. Broadly speaking, if X = (X_1,t,X_2,t;t ≥ 0) is a nonergodic diffusion in R², but there exists a linear combination, say, γ′X, that is instead ergodic in R, then we say there exists a linear stochastic comovement between the components of X. Linear diffusions exhibiting stochastic comovements admit an error correction representation. Estimation of γ and hypothesis testing, under different sampling schemes, are considered.