ARNNResult

class cultivars.univariate.mean_function.ARNNResult(*, endog, fittedvalues, resid, llf, nobs, n_params, order, sigma2, engine, engine_config, predictor)

A fitted neural autoregression.

The model \(y_t = f(y_{t-1}, \ldots, y_{t-p}) + \varepsilon_t\) with \(f\) a learned function and \(\varepsilon_t \sim N(0, \sigma^2)\), the variance concentrated out of a penalized least-squares fit. There is no coefficient vector; the record carries the fitted function as a callable, the fit statistics, and the engine that produced it, since with a plug-in backend the engine is part of the specification.

Variables:

predictor – The learned conditional-mean map, callable through predict().

Note

The inherited fields are endog, fittedvalues, resid, llf, nobs, n_params, order, sigma2, engine and engine_config; the inherited properties r_squared, ssr and parameters_per_observation read them. fittedvalues and resid are aligned with the last nobs = len(endog) - order observations. llf is a concentrated Gaussian likelihood at a penalized fit, so the information criteria compare capacity within one engine configuration and not against a linear model; r_squared is the headline number.

See also

• ARNN – the specification that produces this.

• TARNNResult – one learned function per regime.

• ARResult – the linear case, with coefficients and verdicts.

• NonlinearSSM – what nonlinear_state_space() emits.

Example

A one-lag map \(0.8 \tanh(2 y_{t-1})\) recovered on a grid:

>>> import numpy as np
>>> from cultivars.engine._core._matrices import _lag_matrix
>>> rng = np.random.default_rng(0)
>>> y = np.zeros(500)
>>> for t in range(1, 500):
...     y[t] = 0.8 * np.tanh(2.0 * y[t - 1]) + 0.3 * rng.standard_normal()
>>> res = ARNN(y, order=1).fit()
>>> res.nobs, res.n_learner_parameters, res.engine
(499, 25, 'NumpyMLPEngine')
>>> bool(np.allclose(res.predict(_lag_matrix(y, 1)), res.fittedvalues))
True
>>> grid = np.array([[-1.0], [0.0], [1.0]])
>>> bool(np.max(np.abs(res.predict(grid) - 0.8 * np.tanh(2.0 * grid[:, 0]))) < 0.15)
True

Attributes

predictor	The trained network; use predict() rather than calling it.
endog
engine
engine_config
fittedvalues
information_criteria	AIC, BIC, and HQIC derived from the likelihood and parameter count.
llf
n_learner_parameters	Weights and biases in the single fitted network.
n_params
nobs
order
parameters_per_observation	Nominal learner parameters divided by the effective sample size.
r_squared	Share of the effective sample's variance the fitted mean explains.
resid
sigma2
ssr	Sum of squared residuals over the effective sample.

Methods

compare(*others[, criterion])	Rank this result against others by an information criterion.
likelihood_ratio_test(unrestricted)	Refuse the test: a network's weights are unidentified under a linear null.
nonlinear_state_space(measurement_variance)	The learned mean as a noisily observed state space.
predict(features)	Conditional means for a matrix of lagged levels.
summary()	The estimation summary, renderable as text, HTML, or a dataframe.
to_dict()	The aligned per-observation outputs as plain numpy arrays.
to_pandas(*[, index])	The aligned per-observation outputs as a pandas.DataFrame.
to_polars()	The aligned per-observation outputs as a polars.DataFrame.