Class AlphaStable

Inheritance Relationships

Base Type

Class Documentation

class AlphaStable : public otyca::TimeChangeProcess

Represents an Alpha-Stable time change process.

Public Functions

inline AlphaStable()

Default constructor with alpha initialized to 0.5.

inline AlphaStable(double alpha)

Constructor with a specified alpha parameter.

Parameters:

alpha – Stability parameter (0 < alpha <= 2).

inline virtual AlphaStable *clone() const

Clones the current object.

Returns:

A pointer to the cloned AlphaStable object.

virtual arma::cx_mat laplace_transform(const arma::rowvec &t, const arma::cx_colvec &u, const arma::cx_colvec &psi) const override

Compute the Laplace transform of the process.

The Laplace transform is applied to the time vector, along with Complex-valued column vector of Fourier arguments (u) and the characteristic exponent (psi), to produce the characteristic function (phi).

Parameters:

  • t – The time vector for which the Laplace transform is computed.

  • u – Complex-valued column vector of Fourier arguments.

  • psi – The characteristic exponent.

Returns:

The resulting Laplace-transformed characteristic function.

virtual arma::cx_mat d_phi_d_psi(const arma::rowvec &t, const arma::cx_colvec &u, const arma::cx_colvec &psi) const override

Compute the derivative of the Laplace transform with respect to psi.

This method calculates the derivative of the characteristic function phi with respect to the characteristic exponent psi, and stores the result in d_phi_d_psi.

Parameters:

  • t – The time vector for which the Laplace transform is computed.

  • u – Complex-valued column vector of Fourier arguments.

  • psi – The characteristic exponent.

Returns:

The matrix to store the derivative of the Laplace transform with respect to psi.

virtual std::vector<arma::cx_mat> d_phi_d_p(const arma::rowvec &t, const arma::cx_colvec &u, const arma::cx_colvec &psi) const override

Compute the derivative of the Laplace transform with respect to parameters.

This method computes the derivative of the Laplace transform with respect to its parameters and stores the result in d_phi_d_params.

Parameters:

  • t – The time vector for which the Laplace transform is computed.

  • u – Complex-valued column vector of Fourier arguments.

  • psi – The characteristic exponent.

Returns:

The vector to store the derivatives with respect to parameters.

virtual void set_transformed_calibration_parameters(const std::vector<double> &params)

Sets transformed parameters for the model.

Parameters:

params – Vector of transformed parameter values.

inline virtual void set_parameters(const std::vector<double> &in)

Sets model parameters.

Parameters:

in – Vector containing the alpha parameter.

virtual std::vector<double> transformation_derivatives() const

Computes derivatives of the transformation function.

Returns:

Vector of transformation derivatives.

virtual std::vector<double> get_transformed_calibration_parameters() const

Retrieves the transformed parameters.

Returns:

Vector of transformed parameter values.

inline virtual std::vector<double> get_parameters() const

Retrieves the model parameters.

Returns:

Vector of parameter values.

virtual std::vector<double> get_transformed_calibration_parameter_variances() const

Retrieves the variances of transformed parameters.

Returns:

Vector of variances.

inline virtual std::string name() const

Retrieves the name of the process.

Returns:

The name “AlphaStable”.

inline virtual std::vector<std::string> get_parameter_names() const

Retrieves the names of model parameters.

Returns:

Vector of parameter names.

inline double get_alpha() const

Retrieves the alpha parameter.

Returns:

The alpha value.

inline void set_alpha(double alpha)

Sets the alpha parameter.

Parameters:

alpha – The new alpha value.