Data PDF of stationary process

Let ${\bf R}_N$ be the $N\times N$ covariance matrix of a stationary process. Since the process is stationary, ${\bf R}_N$ will be symmetric and Toeplitz. The PDF may be written as

$$\log p({\bf x}) = -\frac{N}{2} \log (2\pi) - \frac{1}{2}\log \ver... ...det}({\bf R}_N)\vert - \frac{1}{2} {\bf x}^\prime \; {\bf R}_N^{-1} \; {\bf x},$$ (10.6)

where ${\bf R}_N$ is the $N\times N$ covariance matrix of an AR process.