Generalized gamma ARMA process for synthetic aperture radar amplitude and intensity data

We propose a new autoregressive moving average (ARMA) process with generalized gamma (G$\Gamma$) marginal law, called G$\Gamma$-ARMA. We derive some of its mathematical properties: moment-based closed-form expressions, score function, and Fisher information matrix. We provide a procedure for obtaining maximum likelihood estimates for the G$\Gamma$-ARMA parameters. Its performance is quantified and discussed using Monte Carlo experiments, considering (among others) various link functions. Finally, our proposal is applied to solve remote sensing problems using synthetic aperture radar (SAR) imagery. In particular, the G$\Gamma$-ARMA process is applied to real data from images taken in the Munich and San Francisco regions. The results show that G$\Gamma$-ARMA describes the neighborhoods of SAR features better than the gamma-ARMA process (a reference for asymmetric positive data). For pixel ray modeling, our proposal outperforms ${𝒢}_I^0$ and gamma-ARMA.