Two-representation property for non-Gaussian MAG(1) processes

Ascertain whether copula MAG(1) processes with non-Gaussian copulas—defined by V_t = K_{2|1}^{−1}(ε_t | ε_{t−1}) with K a specified bivariate copula and {ε_t} i.i.d. U(0,1)—possess two equivalent representations under permutation of innovations, and, if so, derive the corresponding parameter transformation that maps between the representations.

Background

Beyond the Gaussian case, where two equivalent representations are established, the paper observes from simulations that identifiability behavior may differ for other copulas (e.g., Gumbel), raising a broader theoretical question.

A general result confirming or refuting the existence of two representations for classes of non-Gaussian copulas would have direct implications for identifiability constraints, parameter space restrictions, and consistency arguments in copula-based moving-aggregate models.