MATLAB Programs for Time Series Analysis with AR and ARMA Models

This comprehensive guide details how to implement time series analysis programs for AR and ARMA models using MATLAB. Time series analysis serves as a crucial statistical methodology for investigating patterns and trends in temporally-evolving data. The Autoregressive (AR) model characterizes relationships between current data points and their historical predecessors. The Autoregressive Moving Average (ARMA) model integrates both autoregressive components and moving average features, enabling more accurate future value predictions through sophisticated lag and error term handling. Our MATLAB implementation covers essential workflow stages including data preprocessing techniques (handling missing values, normalization), model parameter estimation using maximum likelihood methods, model fitting validation through residual analysis, and multi-step forecasting procedures. Key functions demonstrated include arima() for model specification, estimate() for parameter optimization, and forecast() for predictive analytics. The programs incorporate practical demonstrations with real-world datasets to validate model performance and interpretation. Through these implementations, you'll gain deeper insights into time series analysis fundamentals and develop practical skills for solving real-world forecasting challenges across domains like finance, economics, and engineering.