The Table Auto-Regressive Moving-Average Model for (Categorical) Stationary Series: Mathematical Perspectives (Invertibility; Maximum Likelihood Estimation)

Abstract

Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.