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