sde_calibration Package

sde_calibration Package

SDE calibration module. It provides an interface for several different methods that are used to infer the drift and diffusion coefficient of a diffusion process. The stochastic process is modelled by an SDE of the following form

\[\mathrm{d}X_t = b(X_t) \mathrm{d}t + \sigma(X_t) \mathrm{d}W_t \ ,\]

where \(X \in \mathbb{R}\), \(W \in \mathbb{R}\) is a standard Wiener process, \(b \colon \mathbb{R} \to \mathbb{R}\) is the drift coefficient, and \(\sigma \colon \mathbb{R} \to \mathbb{R}\) is the diffusion coefficient. The task of calibrating the SDE involves estimating the drift and diffusion coefficient from an observed trajectory of the process \(X_t\). Note that the drift coefficient of the SDE is the same of the corresponding diffusion process. In contrast, the diffusion coefficient of the SDE \(\sigma\) and the corresponding diffusion process \(\Sigma\) are related as follows:

\[\Sigma(x) = \sigma^2(x) \ .\]

See also

For more information on SDEs and diffusion processes, c.f.

estimators Module

class sde_calibration.estimators.Estimator(data, logger=None, **preprocessor_arguments)

Bases: abc.ABC

Abstract base class for any kind of estimator that is used. It defines the basic functionalities like data handling, preprocessing, and logging.

Parameters

  • data (pd.DataFrame) – The time series data that should be used for the estimation. The DataFrame needs to have the fields ‘t’ and ‘X’.

  • logger (logging.Logger, optional) –

    A logger that should be used for logging and/or displaying intermediate resutls.

    |default| None

  • **preprocessor_arguments –

    Keyword arguments that are further passed to the preprocessor class.

Return type

None

Raises

  • TypeError – If the data provided is not of type pandas.DataFarme.

  • KeyError – If the data provided has keys different from t and X.

  • TypeError – If the keyword arguments provided are not valid for the preprocessor class.

abstract fit()

Method that is implement by child classes is order to perform the process of fitting the data. Every estimator is supposed to have this method.

abstract get_num_parameters()

Returns the number of parameters in the model that is used by a certain estimator.

Returns

Number of parameters.

Return type

int

class sde_calibration.estimators.RegressionEstimator(data, logger=None, **preprocessor_arguments)

Bases: sde_calibration.estimators.Estimator

Derived from the Estimator class. This class directly extracts the data and sets up the preprocessor in the form that is required to either estimate the drift or diffusion term. For further information on the parameters see the the documentation of the Estimator.

compile(mode='drift')

Method used to compile the model. For every regression estimator. It is crucial to specify whether the drift or diffusion coefficient should be approximated before the estimator can be fit or called.

Parameters

mode (str, optional) –

A string giving the mode of estimation. Possible options are:

Return type

None

Raises

ValueError – If the provided string for the mode is invalid.

get_mode()

Interface that provides the mode that the regression estimator is currently operating in.

Returns

Returns the current mode. Possible values are:

  • drift

  • diffusion

Return type

str

exceptions Module

exception sde_calibration.exceptions.NotCompiledError

Bases: Exception

Exception that is raised if an estimator is not yet compiled. For many methods this is crucial to compile in order to enable the training and prediction.

Subpackages