Asymptotic Convergence Properties of Autoregressive Moving Average (Arma) Model Estimators

This study investigates the empirical convergence thresholds of the Gaussian Estimation Procedure (GEP), Generalised Least Squares (GLS), and Exact Maximum Likelihood (EML) for ARMA processes. While large-sample asymptotic equivalence is theoretically established, the specific data requirements for numerical reconciliation in higher-order models remain under-researched. Using a generalised Fibonacci-based sampling recurrence  to determine the non-linear sample interval from  to , estimator stability across six distinct data-generating processes was evaluated. The findings demonstrated a ‘complexity-dependent convergence’: while lower-order processes achieved numerical reconciliation at , higher-order ARMA (2,2) specifications require  to achieve harmonization. These results identify a critical transition zone where estimator choice become neural, providing a structural blueprint for selection based on modal dimensionality and available sample size.    

ARMA Models, Likelihood, Asymptotic Theory, Stationarity, Score, Approximation

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