cultivars.spectral.density#
The spectral density of a fitted system: the same model, read by frequency.
A fitted closed system already contains its complete frequency-domain story:
the spectral density matrix f(omega) = Psi(omega) Sigma_u Psi(omega)* /
(2 pi) is a closed form of the coefficients and the innovation covariance,
nothing more. This module reads it out – per-series spectra saying where in
the cycle each variable’s variance lives, coherence saying how tightly two
variables move at each frequency, partial coherence conditioning that
comovement on everything else, and gain and phase giving the lead-lag
reading. In the package’s grammar this is a view, exactly like the
spillover table: construct with any fitted closed reduced-form result – an
OLS VAR, a shrunk BVAR at its posterior mean, a sparse hundred-variable
system – and nothing is re-estimated.
One honesty rule frames every number: a spectrum computed from a fitted model is a statement about the fitted model, inheriting every specification error the time-domain fit carries. No nonparametric periodogram estimation is offered alongside, precisely so the package never blurs which of the two objects a number came from.
References
- Geweke, J. (1982). Measurement of linear dependence and feedback
between multiple time series. Journal of the American Statistical Association, 77(378), 304-313.
- Hamilton, J. D. (1994). Time Series Analysis, chapter 6. Princeton
University Press.
Classes#
The frequency-domain view of any fitted closed reduced form. |
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A fitted system's spectral density matrix, and the readings off it. |