SpectralDensityResult.gain#

SpectralDensityResult.gain(effect, cause)[source]#

The gain of the regression of effect on cause by frequency.

\[G_{ij}(\omega) = \frac{|f_{ij}(\omega)|}{f_{jj}(\omega)},\]

with \(i\) the effect and \(j\) the cause: the amplitude multiplier the best linear frequency-wise predictor of effect from cause applies at each frequency.

Parameters:

  • effect (str) – The variable being explained.

  • cause (str) – The variable explaining it.

Return type:

NDArray[double]

Returns:

A real non-negative (n,) array.

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()
>>> gain = density.gain("gdp", "rate")
>>> gain.shape, bool(np.all(gain >= 0.0)), bool(gain[1] > gain[-1])
((64,), True, True)