Time Series Analysis and Forecasting Using ARMA Models

ARMA (AutoRegressive Moving Average) models represent a fundamental approach for time series analysis and forecasting, widely applied across various practical domains. This methodology enables the utilization of historical data to predict future outcomes, with MATLAB program source code providing an effective implementation framework. The core algorithm involves parameter estimation techniques such as maximum likelihood estimation or least squares methods to optimize model coefficients.

The ARMA model combines autoregressive (AR) and moving average (MA) components to form a linear predictive framework for time series modeling. Its fundamental principle posits that future data points can be expressed as linear combinations of past observations, where the combination coefficients are determined by minimizing prediction errors through computational optimization. Key MATLAB functions for implementation include armax for model estimation and forecast for generating predictions, with model selection criteria like AIC/BIC ensuring optimal parameter identification.

ARMA models find extensive applications in financial market analysis, weather forecasting, stock price prediction, and numerous other fields. In practical implementations, MATLAB source code facilitates efficient model construction and forecasting through built-in functions and customizable scripts. This computational approach significantly enhances workflow efficiency while improving prediction accuracy through automated parameter tuning and residual analysis capabilities. The implementation typically involves data preprocessing, model order identification, parameter estimation, and diagnostic checking stages to ensure robust forecasting performance.