Contribution to statistical inference in ARMA-GARCH random field modeling

In spatial series analysis, accurately modeling regional volatility and spatial dependence structures continue to pose a significant challenge. This article presents a novel quasi-maximum likelihood approach for estimating the coefficients of a two-dimensionally indexed ARMA-GARCH model. Our method is characterized by minimal assumptions when establishing the consistency of the proposed estimators that enhance the flexibility and applicability of the ARMA-GARCH models across diverse data sets. We conducted a Monte Carlo study that validates the theoretical findings of our research, demonstrating its suitability for spatial data scenarios. Our results contribute to advancements in image and signal processing applications, highlighting the broader implications of our work.