Approximation of the covariance matrix $\mathbf{\Sigma}$ of $T$ consecutive observations from a second-order stationary process with continuous positive spectral density $f(\lambda) = \lbrack\sigma^2/(2\pi)^2\rbrack|\sum^\infty_{j=0}\delta_je^{i\lambda j}|^2$ is considered. If $\mathbf{\Sigma}^\ast$ is the covariance matrix corresponding to a process with spectral density $1/\lbrack(2\pi)^2f(\lambda)\rbrack$, then $\mathbf{\Sigma}^\ast - \mathbf{\Sigma}^{-1} \geqq 0$. A matrix $\sigma^{-2}\mathbf{A'A}$ with the property that $\mathbf{\Sigma}^\ast - \sigma^{-2}\mathbf{A'A} - \mathbf{\Sigma}^{-1} \geqq 0$ is also considered. For autoregressive-moving average processes of order $(p, q), \mathbf{\Sigma}^\ast - \sigma^{-2}\mathbf{A'A}$ and $\sigma^{-2}\mathbf{A'A} - \mathbf{\Sigma}^{-1}$ are shown to have rank $\min \lbrack\max (p, q), T\rbrack$ and $\mathbf{\Sigma}^\ast - \mathbf{\Sigma}^{-1}$ to have rank $\min \lbrack 2\max (p, q), T\rbrack$. Some results concerning the covariance determinant are also discussed. If $D_T$ is $\sigma^{-2T}|\mathbf{\Sigma}|$ for sample size $T$ and $D_0 = 1$, then $D_T < D_{T+1}, T = 0, 1, \cdots$, unless the process is autoregressive of order $p$, in which case $1 < D_1 < \cdots < D_p = D_{p+1} = \cdots$.