%0 Journal Article
%T The Table Auto-Regressive Moving-Average Model for (Categorical) Stationary Series: Mathematical Perspectives (Invertibility; Maximum Likelihood Estimation)
%A Chrysoula Dimitriou-Fakalou
%J Open Journal of Statistics
%P 385-407
%@ 2161-7198
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojs.2022.123025
%X 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.
%K Asymptotic Normality
%K Consistency
%K Scores Efficiency
%K Strict Stationarity
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=118121