superstats.transition.stochastic.auto_regression#

Autoregressive transition models.

Classes

AutoRegression([bounds, initial_prior, ...])

AR(1) autoregressive transition.

class superstats.transition.stochastic.auto_regression.AutoRegression(bounds=None, initial_prior=None, sigma=None, phi=None, delta=None)[source]#

Bases: StochasticTransition

AR(1) autoregressive transition.

Parameters:

boundstuple or None, optional, default: None: Lower and upper bounds for the latent state.
initial_priorPrior or None, optional, default: None: Prior for the initial latent state.
sigmafloat or Prior or None, optional, default: None: Standard deviation of the noise.
phifloat or Prior or None, optional, default: None: Autoregressive coefficient.
deltafloat or Prior, optional, default: 0.0: Additive drift term.

Parameters:

bounds (Tuple[float, float] | None)
initial_prior (Prior | None)
sigma (float | Prior | None)
phi (float | Prior | None)
delta (float | Prior | None)

Notes

Implements an AR(1): x_t = phi * x_{t-1} + delta + sigma * eps_t.

sample(batch_size, num_steps)[source]#

Draw batch_size AR(1) trajectories of length num_steps.

Parameters:

batch_sizeint: Number of independent trajectories to draw.
num_stepsint: Number of time steps per trajectory.

Returns:

resultdict - dictionary with keys local_params,: hyper_params, and fixed_params

Parameters:

batch_size (int)
num_steps (int)

Return type:

Dict[str, Any]

sample_one_step(x, params)[source]#

Advance a single AR(1) step.

Parameters:

xfloat: Previous latent state.
paramsdict: Expected keys: sigma, phi, delta.

Returns:

x_nextfloat - the next latent state

Parameters:

x (float)
params (Dict[str, Any])

Return type:

float