SETARResult#

class cultivars.univariate.threshold.SETARResult(*, endog, fittedvalues, resid, llf, nobs, n_params, order, delay, threshold, threshold_values, lower_params, upper_params, sigma2, ssr, self_exciting, n_lower, n_upper, searched_delay)[source]

Bases: _ObservedRegimeResult

A fitted hard-threshold autoregression.

Two linear autoregressions selected by an indicator on a lagged transition variable,

\[\begin{split}y_t = \begin{cases} \phi_L' x_t + \varepsilon_t & z_{t-d} \le r \\ \phi_U' x_t + \varepsilon_t & z_{t-d} > r \end{cases}, \qquad x_t = (1, y_{t-1}, \ldots, y_{t-p})', \quad \varepsilon_t \sim (0, \sigma^2),\end{split}\]

with \(z_t = y_t\) for the self-exciting SETAR and an external series for TAR. Conditional on \((r, d)\) the model is two least-squares problems, so the estimator is a grid search: every candidate threshold on a trimmed quantile grid of the transition variable (and every candidate delay, when the caller left it open) is scored by the total sum of squares and the minimizer is kept. The record stores the split point, the regime assignment and the two coefficient blocks; the inherited fields, the per-regime stability verdicts, the information criteria and the refusal of the likelihood-ratio test come from _ObservedRegimeResult.

Note

The assignment is z <= r to the lower regime, and every reader of the fit – regime_weight, _weight_at, simulate and nonlinear_state_space – uses the same strict comparison on the upper side, so a transition value landing exactly on the threshold is counted as it was when the coefficients were solved for. n_params counts the two coefficient blocks and the threshold, not the variance, so the criteria are comparable with STARResult but sit one parameter below the linear families’ convention. searched_delay is True only when more than one delay was on the grid: SETAR(y, order=1) has nothing to search.

Variables:

  • self_exciting – Whether the transition variable is a lag of the series itself (SETAR) or an external variable (TAR).

  • n_lower – Observations assigned to the lower regime.

  • n_upper – Observations assigned to the upper regime.

  • searched_delay – Whether the delay was chosen by the grid search rather than fixed by the caller.

See also

  • SETAR – the self-exciting model that produces this record.

  • TAR – the externally driven model that produces this record.

  • STARResult – the same two regimes blended by a smooth weight.

  • MarkovSwitchingARResult – regimes driven by a latent chain rather than an observed variable.

References

Tong, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press, ch. 3.

Hansen, B. E. (1997). Inference in TAR models. Studies in Nonlinear Dynamics and Econometrics, 2(1), 1-14.

Example

A two-regime AR(1) with a switch at zero, recovered with its split:

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> y = np.zeros(400)
>>> for t in range(1, 400):
...     phi = 0.6 if y[t - 1] <= 0.0 else -0.4
...     y[t] = phi * y[t - 1] + rng.standard_normal()
>>> res = SETAR(y, order=1, delay=1).fit()
>>> res.self_exciting, res.searched_delay, res.n_lower, res.n_upper, res.nobs
(True, False, 288, 111, 399)
>>> bool(abs(res.threshold) < 0.3), bool(abs(res.lower_params[1] - 0.6) < 0.1)
(True, True)
>>> bool(abs(res.upper_params[1] + 0.4) < 0.25), res.is_regimewise_stationary
(True, True)
>>> res.n_params, round(res.sigma2, 2)
(5, 0.99)

Private methods#

_comparison_label()

Specification label used when this result appears in a ranking.

_from_fit(fit, model)

Assemble the public result from a raw fit and its specification.

_summary_table()

Structured summary rendered by every display path.

_weight_at(z)

Indicator of the upper regime at one transition value.
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