Determinant of Autocorrelation Matrix is Strictly Positive

Theorem
Let $S$ be a strictly stationary stochastic process giving rise to a time series $T$.

Let $\sequence {s_n}$ be a sequence of $n$ successive values of $T$:
 * $\sequence {s_n} = \tuple {z_1, z_2, \dotsb, z_n}$

Let $\mathbf P_n$ denote the autocorrelation matrix associated with $S$ for $\sequence {s_n}$.

The determinant of $\mathbf P_n$ is strictly positive.

Proof
We have that the Autocorrelation Matrix is Positive Definite.

The result follows from Determinant of Positive Definite Matrix is Strictly Positive.