Enhanced Simulation Source Code for ARMA Model with P and Q Order Determination

This enhanced simulation source code for ARMA models incorporates significant improvements to achieve comprehensive determination of optimal P and Q orders. Specifically, we implement more precise and refined algorithms such as the Least Squares Method to optimize model accuracy and precision. The implementation includes automated order selection algorithms that systematically evaluate different (P,Q) combinations using information criteria like AIC or BIC. For data processing, we introduce more comprehensive and thorough data collection and analysis procedures, including robust preprocessing routines that handle stationarity checks, differencing operations, and outlier detection to ensure model reliability and stability. The code incorporates advanced validation techniques including cross-validation and residual analysis modules. Furthermore, we conduct in-depth exploration and analysis of both algorithms and models through detailed diagnostic functions that examine autocorrelation functions (ACF) and partial autocorrelation functions (PACF) of residuals. This enables the discovery of additional latent information and application scenarios, providing valuable references and insights for research and practical applications in related fields. The implementation includes modular functions for model comparison, forecast error analysis, and scenario simulation capabilities.