Determining Model Order in AR Model Algorithm

In time series analysis, the AR (Autoregressive) model is a fundamental modeling approach where determining the model order (i.e., the number of lag terms) is crucial. The Akaike Information Criterion (AIC) is widely used for evaluating model goodness-of-fit versus complexity, particularly suitable for AR model order selection.

AIC calculation is based on the model's likelihood function while accounting for the number of parameters. The formula is: AIC = -2 × ln(maximum likelihood) + 2 × number of parameters. A lower AIC value indicates a better balance between model fit and complexity.

In AR models, increasing the order may improve fitting performance, but excessive parameters can cause overfitting. AIC addresses this through its penalty term (2 × parameter count) to discourage overly complex models, thereby facilitating optimal order selection. In practice, developers can implement this by testing AR models with different orders, computing AIC values for each, and selecting the order yielding the minimum AIC. This can be automated using functions like MATLAB's aic or Python's statsmodels ARIMA implementation which returns AIC metrics.

While AIC's strength lies in its general applicability and computational simplicity, it's important to note its preference for moderate sample sizes. For small datasets, the corrected AICc criterion should be considered, which adds a finite-sample adjustment term to reduce bias.