MATLAB Code Implementation for AR Spectrum Estimation Function

In this section, we introduce the AR spectrum estimation function, an essential tool for understanding autoregressive model fitting. This function incorporates three distinct criteria for optimal AR order selection: FPE (Final Prediction Error), AIC (Akaike Information Criterion), and CAT (Criterion Autoregressive Transfer) criteria. The FPE criterion operates on the principle of minimizing the mean square error of predictions, making it suitable for forecasting applications. The AIC criterion employs information theory to balance model complexity and goodness-of-fit, preventing overfitting. The CAT criterion utilizes a weighted average of multiple statistical measures to determine the optimal model order. From an implementation perspective, the function typically accepts time series data as input and returns the estimated power spectral density. Key MATLAB functions involved may include `aryule` for Yule-Walker algorithm implementation or `arburg` for Burg's method, combined with custom code for criterion evaluation. The algorithm workflow generally involves: 1) computing AR coefficients for different orders, 2) calculating criterion values for each order, and 3) selecting the order with the minimum criterion value. When using the AR spectrum estimation function, practitioners can select the appropriate criterion based on their specific application requirements to achieve optimal modeling results. For instance, AIC is preferable for general-purpose modeling while FPE excels in prediction-focused scenarios.