Simulation of Least Squares Estimation for AR Parameters in ARMA Models Using Observational Data

This program performs simulation-based estimation of AR parameters in ARMA models from observational data using least squares methods, handling both known and unknown parameter scenarios. The implementation leverages sophisticated mathematical algorithms including Kalman filtering for state estimation, Fourier transforms for frequency-domain analysis, and stochastic process modeling for handling random components. The code structure facilitates various simulation experiments and data analysis tasks such as model comparison through likelihood ratio tests, parameter optimization via gradient descent algorithms, and error analysis using residual diagnostics. Additionally, the program incorporates statistical validation methods including confidence interval calculation and hypothesis testing for parameter significance. This makes it a highly efficient and robust tool suitable for diverse scientific research and engineering applications, particularly in time series analysis and system identification projects.