= Cross-spectrum of two stationary time series
{title2=$f_{XY}(\lambda)=\frac1{2\pi}\sum_h\mathbb E[X_tY_{t+h}]e^{-ih\lambda}$}
= Cross-spectrum
{synonym}
For zero-mean real <weakly stationary processes> whose cross-covariances are summable, the cross-spectrum is the <Fourier series> of their lagged <covariance>, with the displayed convention. Reality gives $f_{XY}(-\lambda)=\overline{f_{XY}(\lambda)}$, but the cross-spectrum need not be real or even. Exchanging the two series gives $f_{YX}(\lambda)=\overline{f_{XY}(\lambda)}$. The entries form a Hermitian <spectral density of a stationary process> matrix.
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