Time Series Forecasting Using Autoregressive Moving Average (ARMA) Models

This MATLAB program implements autoregressive moving average (ARMA) modeling for time series forecasting, providing a statistical framework to analyze sequential data points collected over time. The implementation includes key functions for model identification, parameter estimation, and prediction generation. The program architecture begins with data preprocessing and stationarity checks, followed by model order selection using information criteria like AIC or BIC. The core algorithm employs maximum likelihood estimation or least squares methods to calibrate autoregressive (AR) and moving average (MA) parameters based on historical patterns. The forecasting engine then generates future values by combining past observations (AR component) and error terms (MA component) through difference equations. Key computational components include: - armax function for model parameter estimation - forecast method for multi-step predictions - Residual analysis for model validation - Confidence interval calculation for uncertainty quantification The implementation outputs refined forecasts with statistical metrics, enabling data-driven decision making based on predicted future values. This provides researchers and analysts with a robust toolbox for understanding temporal patterns, seasonal variations, and trend developments in time series data.