cultivars.univariate

Univariate models: one series, its mean, its variance, and its components.

Every model here takes one observed series and answers one of three questions about it. What drives its conditional mean: a linear autoregression (autoregression), the Box-Jenkins family with differencing, seasonality and regressors (box_jenkins), long memory through a fractional difference (fractional_integration), a regime that switches on an observed variable, abruptly (threshold) or smoothly (smooth_transition), a regime that switches on a latent Markov chain (regime_switching), or a learned nonlinear function of the lags (mean_function). What drives its conditional variance: a deterministic recursion on past shocks (conditional_variance) or a latent process with its own innovation (stochastic_volatility). Or what it is made of: a trend, a cycle, a seasonal and an irregular, each with a likelihood and a band (unobserved_components).

The models share one shape. A model object holds the specification and nothing else; fit (or sample, for the Bayesian estimators) returns an immutable record that carries the estimates, the fit statistics and the aligned per-observation series, and that record is the only thing a consumer ever reads. Every record renders the same way (print, a notebook cell, summary().to_pandas()), exposes its series the same way (to_pandas, to_polars), ranks against other records fitted on the same sample with compare and information_criteria, and – where the model has a state-space reading – emits it as a state_space system that can filter data it was not estimated on. Refusals are typed: a test whose null distribution does not exist for the model raises rather than returning a number, and a comparison across different effective samples raises rather than ranking incomparable likelihoods.

Names are imported from the leaf module, never from here – from cultivars.univariate.box_jenkins import ARIMA – so an import path names the family, the specification and the class. This package exposes only the modules.

Layout. The public classes are thin: each validates its specification on a model base in cultivars._internals and assembles its public record from a packed fit, while the objectives, solvers, simulators, system builders and the shared result mixins live in _internals and the numerical primitives in _core. Diagnostics to run before a fit are in diagnostics; the forecast evaluation that reads these records is in forecast; the vector counterparts of the mean models are in multivariate.

Example

A linear and a threshold autoregression on one sample, ranked by BIC through the shared comparison surface:

>>> 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()
>>> linear = autoregression.AR(y, order=1).fit()
>>> hard = threshold.SETAR(y, order=1, delay=1).fit()
>>> table = linear.compare(hard, criterion="bic")
>>> [row[0] for row in table.rows]
['SETAR(1, d=1)', 'AR(1)']
>>> list(hard.to_pandas().columns)
['observed', 'fitted', 'resid', 'threshold_variable', 'regime_weight']

Modules

autoregression	Autoregressive model AR(p) -- the public specification and result.
box_jenkins	ARMA / ARIMA / SARIMA / SARIMAX -- one engine behind four public fronts.
conditional_variance	Conditional-variance models: GARCH, GJR, EGARCH, and FIGARCH.
fractional_integration	ARFIMA(p, d, q) -- fractionally integrated ARMA with long memory.
mean_function	Learned conditional means: AR-NN and TAR-NN.
regime_switching	Markov-switching autoregression: the latent-regime counterpart to SETAR.
smooth_transition	Smooth-transition autoregressions: LSTAR and ESTAR.
stochastic_volatility	Stochastic volatility: variance as a latent state, not a function of the past.
threshold	Threshold autoregressions: SETAR and TAR.
unobserved_components	Structural time series: decomposition with a likelihood.