cultivars.multivariate

Multivariate time series: one closed-system contract, five families on it.

Every model in this package estimates how a vector of series moves together, and every one of them is organized around a single contract. A fitted reduced form is a closed system: it exposes its variable names, its coefficient stack, its innovation covariance \(\Sigma_u\), its residuals and its moving-average representation \(\Psi_h\), and everything downstream – structural identification, regime views, connectedness networks – consumes that protocol rather than a particular class. The families differ in what they assume about the coefficients. reduced_form is the least-squares core: the VAR and VARX, the error-correction form for cointegrated levels, the vector moving average, mixed frequencies, panels, the closed global VAR, functional and term-structure designs, each a different \(X\) on one estimator. large_dim is what to do when \(p k^2\) coefficients outrun the sample: shrink them toward a prior, set most of them to zero, or factor the panel. nonlinear lets the coefficients depend on an observable state, a quantile level or the date. regime_switching lets them switch with a latent Markov chain, and returns a posterior over regimes rather than a chronology. structural is where the shocks acquire names: declared zeros, declared signs, outside instruments, or statistical properties of the innovations, applied to any closed system, plus the DSGE whose structure is a solved model.

Two commitments run through every family. First, estimation and identification are separate acts. A reduced form is fitted once and reports only what the data determine; a structural scheme is constructed from that result, declares what it adds, and restates the declaration in its summary, so an impulse response can always be traced back to the assumption that signed it. Second, a result is an immutable record that renders the same way everywhere and refuses what it cannot support: a partially identified scheme carries only the columns it identified, a set-identified scheme returns the set, a mixture refuses the regime-count test its likelihood cannot answer, and a long-run restriction refuses a unit root. The packages re-export modules only; import a model from its module.

Example

A reduced form fitted once, then read three ways – its own orthogonalized responses, a declared recursive identification, and a Diebold-Yilmaz connectedness view – all from the same record:

>>> import numpy as np
>>> from cultivars.multivariate.reduced_form.vector_autoregression import VAR
>>> from cultivars.multivariate.structural.zero_restrictions import RecursiveSVAR
>>> from cultivars.multivariate.large_dim.spillover import Spillover
>>> rng = np.random.default_rng(0)
>>> B = np.array([[1.0, 0.0], [0.5, 1.0]])
>>> y = np.zeros((402, 2))
>>> for t in range(1, 402):
...     y[t] = 0.4 * y[t - 1] + B @ rng.standard_normal(2)
>>> res = VAR(y, order=1, names=("r", "x")).fit()
>>> svar = RecursiveSVAR(res).identify()
>>> bool(np.allclose(svar.irf(4), res.irf(4, orthogonalized=True)))
True
>>> network = Spillover(res, horizon=10).compute()
>>> network.table.shape, bool(0.0 <= network.total <= 100.0)
((2, 2), True)

Modules

large_dim	Large-dimensional multivariate models: shrink, select, or factor the panel.
nonlinear	Nonlinear multivariate models: coefficients that depend on a state, a quantile, or the date.
reduced_form	Reduced-form multivariate models: one least-squares surface, eight designs.
regime_switching	Latent-regime multivariate models: the regime inferred, never observed.
structural	Structural identification: what the data cannot supply, declared or tested.