AR, MA, ARMA Models and Simulation Programs

This repository contains AR (Autoregressive), MA (Moving Average), and ARMA (Autoregressive Moving Average) models with corresponding simulation programs, which are fundamental tools for time series analysis. The AR model predicts future values based on linear combinations of past observations, typically implemented using recursion formulas or least squares estimation. The MA model uses past error terms for forecasting, often calculated through innovation algorithms or maximum likelihood estimation. The ARMA model combines both approaches, requiring parameter optimization techniques like the Box-Jenkins methodology for model fitting. These models are widely used for forecasting future trends and behaviors, making them valuable for economists and data scientists. The simulation programs enable testing model performance through synthetic time series generation, allowing users to validate assumptions and understand practical applications through controlled experiments. The code implementation includes key functions for parameter estimation, residual calculation, and predictive diagnostics to facilitate hands-on learning. We hope these resources support your study and research in time series analysis!