= Spectral distribution function of a stationary time series
{title2=$F(\lambda)=\mathcal F([-\pi,\lambda])$}
= Time-series spectral distribution
{synonym}
The cumulative function of the finite positive <spectral measure of a stationary time series> is nondecreasing and right-continuous, with total mass equal to the variance. For an absolutely continuous measure, $F(\lambda)=\int_{-\pi}^{\lambda}f(u)du$, where $f$ is the <time-series spectral density>. Under angular-frequency normalization, $\gamma_k=\int_{-\pi}^{\pi}e^{ik\lambda}dF(\lambda)$ and, when the covariance series is absolutely summable, $f(\lambda)=(2\pi)^{-1}\sum_{k\in\mathbb Z}\gamma_k e^{-ik\lambda}$. Atoms describe persistent periodic components and cannot be represented by an ordinary density.
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