Training ARMAX model based on the Schur-Cohn algorithm to guarantee stability

The AutoRegressive Moving Average model with eXogenous inputs (ARMAX) is a well-established linear input-output model formulation for time series analysis. This project implements the Schur-Cohn transform algorithm in C++ to detect and analyze the stability of polynomial coefficients of the AutoRegressive (AR) and Moving Average (MA) components within an ARMAX model. Based on this algorithm, an optimization approach is proposed to improve ARMAX model performance under user-specified parameter constraints. The implementations aim to provide an effective computational framework for investigating ARMAX model stability and enhancing model accuracy in time series forecasting. The efficacy of the proposed methodology is validated empirically through model implementation and forecasting performance evaluation on a designated experimental dataset.