Stochastic Differential Modeling Module

class experimentalis.extension.sde.DriftNet(*args, **kwargs)

Bases: Model

This is a drift network form for automatically learning the stochastic drift \(\mu\) from the data rather than manually guessing, as a means to curb the local-minima issue resulting from the naive model.

Parameters:

hidden_units (int) – The number of hidden units (weight + bias) to use in the model, effectively a measure of the model’s complexity.

call(t)
class experimentalis.extension.sde.GBM(initial_value, drift, volatility, drift_bounds=(-1.0, 1.0), volatility_bounds=(1e-06, 2.0))

Bases: IntegratedItoSDEModel

This is a very generic stochastic differential equation (SDE) model in 1D using Geometric Brownian Motion. (GBM) in integrated form.

Example:

# some time-series dataset with inherent randomness
dataset = Dataset(...)

...

model = GBM(
    initial_value = prices[0],
    drift = 1.01e-3,             # very small drift, i.e., predictibility
    drift_bounds = (0,0.1),      # depending on data, drift is usually small
    volatility = 2e-2,           # higher volatility
    volatility_bounds = (0,1)    # volatility can be higher, but this makes sense for the data
)

result = autofit(dataset, model, graphing_options=g_opts)
...
class experimentalis.extension.sde.IntegratedItoSDEModel(integrated_function, initial_value, param_names, param_values, param_bounds=None)

Bases: Model

This is a base class for implementing various superclass models in the family of stochastic PDEs, as solved via Ito’s lemma, following the equation

\[dS_t = \mu(S_t, t) dt + \sigma(S_t, t) dB_t\]
evaluate(t, *params)

Evaluates the SDE integrated solution with the given parameters.

Parameters:

  • t (NDArray) – Array of times to evaluate on

  • params (float or NDArray) – Parameter values

class experimentalis.extension.sde.LearnedDriftGBM(initial_value, volatility, hidden_units=8, volatility_bounds=(1e-06, 2.0), weight_init_scale=0.1, use_cpu=False)

Bases: Model

This is another implementation of the integrated Geometric Brownian Motion model for a stochastic differential dataset, but in this case, the drift parameter \(\mu\) is learned from the data using machine learning, and only the volatility \(\sigma\) is set manually.

evaluate(t, volatility, *weights)

Simultaneously trains the model and evaluates it on the present data.

Parameters:

  • t (float or NDArray) – The time data to evaluate at.

  • volatility (float) – The volatility of the data.

  • weights (NDArray or float) – The current weights of the data.

experimentalis.extension.sde.gbm_function(t, initial_value, drift, volatility)

Implementation of the GBM equation

\[S_t = S_0 \exp\left\{\sigma B_t + \left( \mu - \frac{\sigma^2}{2} \right) t\right\}\]
Parameters:

  • t (NDArray) – The time values to evaluate on

  • initial_value (float) – \(S_0\) The initial value

  • drift – \(\mu\) The percentage drift (predictability).

  • volatility (float) – \(\sigma\) The percentage volatility of the dataset.

  • drift_bounds (tuple[float, float] or None) – Optional bounds on the geometric drift.

  • volatility_bounds (tuple[float, float] or None) – Optional bounds on the volatility.