Autoregressive Models

Fit a classical AR or threshold AR model, or learn time-varying coefficients and order with DeepLagField. See DeepLagField for a complete training example.

Linear AR

class neuralfieldmanifold.models.AR(*, order)

Ordinary least-squares autoregressive model with an intercept.

Parameters:

order (int) – Number of lagged samples used to predict the next sample.

Notes

Call fit to estimate the intercept and coefficients and obtain an ARFit.

fit(signal)

Estimate the intercept and lag coefficients by ordinary least squares.

class neuralfieldmanifold.models.ARFit(intercept: float, coefficients: ndarray)

Fitted AR intercept and coefficients, ordered from lag 1 onward.

predict(signal)

One-step predictions, aligned to signal[order:].

forecast(signal, *, start_sample, n_samples, refresh_samples=None)

Forecast recursively, optionally refreshing the observed lag history.

Parameters:

• signal (array_like) – Observed signal providing the initial lag history and any refreshes.

• start_sample (int) – Index of the first predicted sample.

• n_samples (int) – Number of predictions.

• refresh_samples (int or None) – Number of predictions between observed-history refreshes. None gives a free-running forecast; 1 gives one-step prediction at every sample.

Returns:

Predictions beginning at start_sample.

Return type:

ndarray, shape (n_samples,)

information_criteria(signal)

Return AIC and BIC on the supplied signal using order + 1 parameters.

class neuralfieldmanifold.models.PredictionMetrics(mse: float, mae: float, correlation: float)

Mean squared error, mean absolute error, and Pearson correlation.

neuralfieldmanifold.models.prediction_metrics(observed, predicted)

Compare equal-length one-dimensional observed and predicted signals.

Threshold AR

class neuralfieldmanifold.models.TAR(*, order, delay_samples=1, threshold=0.0)

Fit two AR regimes separated by a delayed signal threshold.

Parameters:

• order (int) – AR order in each regime.

• delay_samples (int) – Lag used for threshold comparison, between 1 and order.

• threshold (float) – Values at or below the threshold use the lower regime.

fit(signal)

Estimate both regimes by least squares and return a TARFit.

class neuralfieldmanifold.models.TARFit(lower: ARFit, upper: ARFit, threshold: float, delay_samples: int, lower_residuals: ndarray, upper_residuals: ndarray)

Lower and upper AR regimes, threshold, delay, and residual pools.

simulate(initial_lags, *, n_samples, seed=0, match_reference=None)

Simulate with bootstrapped residuals and newest-first initial lags.

If match_reference is supplied, the generated signal is rescaled to its mean and standard deviation. This rescaling is intended for distribution-matched simulation, not held-out forecast evaluation.

DeepLagField

class neuralfieldmanifold.models.DeepLagField(*, sequence_length=600, orders=(2, 3, 4, 5, 6), hidden_size=128)

Jointly estimate AR order and time-varying coefficients.

Parameters:

• sequence_length (int) – Number of time samples per input sequence.

• orders (tuple of int) – Increasing candidate AR orders, each smaller than sequence_length.

• hidden_size (int) – Hidden width of the order and dynamics multilayer perceptrons.

Notes

The order network selects a lag mask that conditions the dynamics network. Coefficients beyond the selected order are zeroed. Training uses hard straight-through Gumbel sampling; evaluation uses argmax unless sample_order=True is passed to forward.

forward(x, *, temperature=1.0, sample_order=None)

Estimate coefficients, select orders, and reconstruct each sequence.

Parameters:

• x (torch.Tensor, shape (batch, sequence_length)) – Floating-point input sequences.

• temperature (float) – Positive temperature for Gumbel sampling.

• sample_order (bool or None) – Sample orders if True, or use argmax if False. None samples in training mode and uses argmax in evaluation mode.

Returns:

Coefficients, order logits, selected orders, and predictions.

Return type:

DynamicsOutput

save(path)

Save architecture settings and weights, without optimizer state.

classmethod load(path, *, device='cpu')

Load a package checkpoint in deterministic evaluation mode.

class neuralfieldmanifold.models.DynamicsOutput(coefficients: Tensor, order_logits: Tensor, order: Tensor, prediction: Tensor)

Predicted dynamics for a batch of input sequences.

coefficients

Lag-1-first coefficients, masked beyond each selected order.

Type:

torch.Tensor, shape (batch, time, max_order)

order_logits

Unnormalized order-selection scores.

Type:

torch.Tensor, shape (batch, n_orders)

order

Selected AR order for each sequence.

Type:

torch.Tensor, shape (batch,)

prediction

AR reconstruction using observed lag history. Missing history at the start of the sequence is zero-padded.

Type:

torch.Tensor, shape (batch, time)