CR Bound (FIM)

To apply (2.27), we need the FIM or the CR bound covariance (inverse of FIM). The CR bound for AR parameters is well known [31]. We have

$${\bf C}_{\bf a} = \frac{N}{\sigma^2}{\bf R},$$

where ${\bf R}$ is the $P\times P$ auto-correlation matrix. Note that $\frac{1}{\sigma^2}{\bf R}$ has asymptotically determinant 1.

The CR bound for $\sigma^2$ is independent of ${\bf C}_a$ and given by

$${\bf C}_{\sigma^2}=\frac{2\sigma^4}{N}.$$

The function software/module_ar_ml.m implements this. We compare this method with other approaches in Section 10.4.10.