Determinant of Autocorrelation Matrix is Strictly Positive/Examples/Order 3

Example of Use of Determinant of Autocorrelation Matrix is Strictly Positive
Let $\rho_k$ denote the autocorrelation of a strictly stationary stochastic process $S$ at lag $1k$.

Then:
 * $-1 < \rho_1 < 1$
 * $-1 < \rho_2 < 1$
 * $-1 < \dfrac {\rho_2 - \rho_1^2} {1 - \rho_1^2} < 1$

Proof
Consider the autocorrelation matrix of order $3$:

Also from:

the other conditions follow from the order $2$ case.