Estimating ARIMA Models in Time Series Analysis Using Maximum Log-Likelihood Estimation Method

This resource provides MATLAB source code for estimating ARIMA (AutoRegressive Integrated Moving Average) models in time series analysis using the maximum log-likelihood estimation method. The implementation includes parameter estimation algorithms that optimize model coefficients through numerical optimization techniques, and model selection mechanisms that compare different ARIMA specifications using information criteria such as AIC or BIC. This method is widely applied in financial analysis, economic forecasting, and various data analysis domains for its statistical efficiency and robustness. The code structure typically involves functions for differencing time series to achieve stationarity, estimating autoregressive (AR) and moving average (MA) parameters using optimization routines like fmincon or fminunc, and calculating likelihood functions with proper error term handling. Prior to using this source code, users should have fundamental MATLAB programming skills and understanding of time series concepts including stationarity, autocorrelation functions, and model identification techniques. If you encounter any issues during implementation, consult MATLAB documentation on optimization functions and time series analysis literature covering maximum likelihood estimation principles. Professional statistical software documentation may also provide additional insights. We encourage users to share experiences and discuss code modifications to enhance practical applications in real-world scenarios, potentially extending the code to include seasonal components (SARIMA) or exogenous variables (ARIMAX).