SpectralDensityResult.coherence#

SpectralDensityResult.coherence(first, second)[source]#

Squared coherence between two variables, in [0, 1].

\[C_{ij}(\omega) = \frac{|f_{ij}(\omega)|^2}{f_{ii}(\omega)\, f_{jj}(\omega)},\]

the frequency-domain analogue of a squared correlation – how much of the two variables’ power at each frequency is shared. Symmetric, and silent about direction; the directional reading belongs to SpectralCausality.

Parameters:

  • first (str) – An endogenous variable.

  • second (str) – Another endogenous variable.

Return type:

NDArray[double]

Returns:

A real (n,) array in [0, 1].

Raises:

SpecificationError – If either label is unknown.

Example

>>> import numpy as np
>>> from cultivars.multivariate.reduced_form.vector_autoregression import VAR
>>> rng = np.random.default_rng(0)
>>> y = np.zeros((500, 2))
>>> for t in range(1, 500):
...     y[t, 0] = 0.5 * y[t - 1, 0] + 0.4 * y[t - 1, 1] + rng.standard_normal()
...     y[t, 1] = 0.5 * y[t - 1, 1] + rng.standard_normal()
>>> res = VAR(y, order=1, names=("gdp", "rate")).fit()
>>> density = SpectralDensity(res, n_frequencies=64).compute()
>>> forward = density.coherence("gdp", "rate")
>>> bool(np.allclose(forward, density.coherence("rate", "gdp")))
True
>>> bool(np.all((forward >= 0.0) & (forward <= 1.0)))
True