On the residual variance and the prediction error for the LSF estimation method and new modified finite sample criteria for autoregressive model order selection

The case where the data sample size is finite and the least-squares-forward (LSF) method is used for autoregressive (AR) parameter estimation is considered. New formulas describing the residual variance and the prediction error behaviors in AR parameter estimation are derived, and the relation between the residual variance and the prediction error is determined. Based on this relation, the existing finite sample criteria for AR model order selection are modified, and it is shown that these modified criteria have better performance.