Parameter Estimation Methods for Stationary Time Series with MATLAB Implementation

To ensure accurate estimates and predictions for parameters in stationary time series, appropriate estimation and forecasting methods are essential. Key estimation techniques include moment estimation (implemented using sample moment matching with functions like mean() and var()) and maximum likelihood estimation (optimized through fmincon() or mle() functions). Forecasting methods comprise differential equation approaches (solved using ode solvers), inverse function techniques (implemented with numerical inversion algorithms), and Green's function methods (calculated via convolution operations). To enhance usability and accessibility, we recommend MATLAB implementation featuring structured functions for each method, complete with error handling and visualization capabilities. This programming approach enables efficient application across various scenarios, with code modules handling data preprocessing, parameter optimization, and prediction accuracy validation through metrics like MSE and confidence intervals.