SparseVAR.fit#

SparseVAR.fit(*, penalty='lasso', lam=None, n_lambdas=20, lambda_min_ratio=1e-3)[source]#

Estimate under one penalty family, selecting the level if unstated.

Parameters:

  • penalty (Literal['lasso', 'adaptive', 'scad', 'mcp', 'group']) – "lasso", "adaptive", "scad", "mcp", or "group" (the lag-group penalty, which selects whole lags).

  • lam (float | None) – Penalty level, positive, or None for rolling-origin selection.

  • n_lambdas (int) – Candidate levels on the geometric path, at least 2.

  • lambda_min_ratio (float) – Smallest candidate as a fraction of the level that zeroes everything, in (0, 1).

Return type:

SparseVARResult

Returns:

The fitted SparseVARResult.

Raises:

  • SpecificationError – If the penalty specification is malformed or the sample cannot support the rolling validation.

  • NumericalError – If the solver loses curvature.

Example

The nonconvex penalties keep fewer coefficients than the lasso at their selected levels, and the group penalty keeps or drops whole lags:

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> k, n = 6, 300
>>> first = 0.5 * np.eye(k)
>>> first[1, 0], first[3, 2] = 0.3, -0.3
>>> y = np.zeros((n, k))
>>> for t in range(1, n):
...     y[t] = first @ y[t - 1] + rng.standard_normal(k)
>>> model = SparseVAR(y, order=2)
>>> lasso = model.fit(penalty="lasso")
>>> mcp = model.fit(penalty="mcp")
>>> bool(mcp.n_nonzero < lasso.n_nonzero)
True
>>> grouped = model.fit(penalty="group")
>>> per_lag = [int(np.count_nonzero(block)) for block in grouped.coefficients]
>>> all(count in (0, k * k) for count in per_lag)
True
>>> model.fit(lam=0.0)
Traceback (most recent call last):
cultivars.exceptions.SpecificationError: lam must be positive when given; got 0.0.
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