Free deterministic equivalent Z-scores of compound Wishart models: A goodness of fit test of 2DARMA models

We introduce a new method to qualify the goodness of fit parameter estimation of compound Wishart models. Our method based on the free deterministic equivalent Z-score, which we introduce in this paper. Furthermore, an application to two dimensional autoregressive moving-average model is provided. Our proposal method is a generalization of statistical hypothesis testing to one dimensional moving average model based on fluctuations of real compound Wishart matrices, which is a recent result by Hasegawa, Sakuma and Yoshida.