Triangular spectral density of a stationary time series ($f(\lambda )=\pi -|\lambda |(-\pi \le \lambda \le \pi )$)

Under angular-frequency normalization, the displayed time-series spectral density gives ${\gamma }_0={\pi }^2$ and ${\gamma }_k=2(1-(-1{)}^k)/k^2$ for nonzero integer $k$. This follows from the even integral $2{\int }_0^{\pi }(\pi -\lambda )\cos (k\lambda )d\lambda$. All nonzero even-lag covariances vanish while the odd-lag covariances are positive.