MATLAB Code Implementation for ARMA Prediction with Second-Order Differencing

This example demonstrates an ARMA prediction algorithm implementation for forecasting oil prices using second-order differencing. The core algorithm involves implementing AutoRegressive Moving Average modeling through functions like aryule() for autoregressive parameter estimation and armax() for model fitting. The preprocessing stage applies second-order differencing using diff(data,2) to achieve stationarity in the time series data. Key implementation steps include: determining optimal ARMA orders via autocorrelation/partial autocorrelation analysis, parameter estimation using maximum likelihood methods, and generating forecasts with prediction error bounds. The code structure allows for adjusting critical parameters including AR order (p), MA order (q), and differencing degree to optimize forecast accuracy. This case study provides practical insights into time series decomposition, model diagnostics through residual analysis, and interpretation of forecast results with confidence intervals. Users can modify the algorithm to experiment with different optimization techniques like AIC/BIC criteria for model selection and explore various initialization methods for enhanced prediction performance.