Determining Time Series Order Using FPE or AIC Criterion with MATLAB Implementation

Using FPE or AIC criteria to determine the order of time series in MATLAB serves as a valuable analytical tool. The implementation typically involves calculating information criteria across different model orders and selecting the one that minimizes the criterion value. Key MATLAB functions like `aicbic()` or custom implementations using `armax()` for model fitting can be employed. During the process, you should address outlier handling through techniques such as robust regression or data transformation, and optimize computations using vectorized operations. The code structure generally involves: 1) iterating through potential orders, 2) fitting corresponding AR/ARMA models, 3) computing criterion values, and 4) identifying the optimal order. You may explore alternative order selection criteria like BIC or MDL to compare performance metrics and accuracy. If uncertain, consult MATLAB documentation or online resources detailing functions like `aryule()` for autocorrelation-based estimation or `arima()` for comprehensive time series modeling. Once the optimal order is determined, it facilitates model construction using System Identification Toolbox functions, enabling forecasting and trend analysis through methods such as `predict()` or `forecast()`. This provides deeper insights into time series characteristics through residual analysis and model validation techniques.