Determinant of Autocorrelation Matrix is Strictly Positive/Examples

Examples of Use of Determinant of Autocorrelation Matrix is Strictly Positive

Order $2$

Let $\rho_1$ be the autocorrelation of a strictly stationary stochastic process $S$ at lag $1$.

Then:

$-1 < \rho_1 < 1$

Order $3$

Let $\rho_k$ denote the autocorrelation of a strictly stationary stochastic process $S$ at lag $1k$.

Then:

$-1 < \rho_1 < 1$

$-1 < \rho_2 < 1$

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