Model ct

CT model class.

`CentTend`

Bases: SDE

Central Tendency model.

`init(param=None)`

Initialize the class.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	True parameters used for simulation of the data	`None`

`coef_big_as(*, param, aggh)` `staticmethod`

Coefficient A^\sigma_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient A^\sigma_h

`coef_big_ay(*, param, aggh)` `staticmethod`

Coefficient A^v_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`coef_big_bs(*, param, aggh)`

Coefficient B^\sigma_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient B^\sigma_h

`coef_big_cs(*, param, aggh)`

Coefficient C^s_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient C^s_h

`coef_big_cy(*, param, aggh)`

Coefficient C^y_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient C^y_h

`coef_small_as(*, param, aggh)`

Coefficient a^s_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient a^s_h

`coef_small_ay(*, param, aggh)`

Coefficient a^v_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`coef_small_bs(*, param, aggh)`

Coefficient b^s_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient b^s_h

`coef_small_cs(*, param, aggh)`

Coefficient c^s_h in exact discretization of volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`	Coefficient c^s_h

`get_start()`

Return starting values for simulation.

`mat_a(*, param, subset=None)`

Matrix A in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`subset`	`slice`	Which moments to use	`None`

Returns:

Type	Description
`(nmoms, 3*nmoms) array`	Matrix A

`mat_a0(*, param, aggh)`

Matrix A_0 in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`(4, 4) array`	Matrix A_0

`mat_a1(*, param, aggh)`

Matrix A_1 in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`(4, 4) array`	Matrix A_1

`mat_a2(*, param, aggh)`

Matrix A_2 in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`(4, 4) array`	Matrix A_2

`mat_a3(*, param, aggh)`

Matrix A_3 in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`(4, 4) array`	Matrix A_3

`mat_a4(*, param, aggh)`

Matrix A_4 in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`(4, 4) array`	Matrix A_4

`mat_a5(*, param, aggh)`

Matrix A_5 in integrated moments.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`(4, 4) array`	Matrix A_5

`mean_cross(*, param, aggh)`

Unconditional mean of realized returns times volatility.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`mean_ret(*, param, aggh)` `staticmethod`

Unconditional mean of realized returns.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`mean_vol(*, param, aggh)` `staticmethod`

Unconditional mean of realized volatiliy.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`mean_vol2(*, param, aggh)`

Unconditional mean of squared realized volatiliy.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`realized_const(*, param=None, aggh=1, subset=None)`

Intercept in the realized moment conditions.

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	`None`
`aggh`	`float`	Interval length	`1`
`subset`	`slice`	Which moments to use	`None`

Returns:

Type	Description
`(4, ) array`	Intercept

`realized_depvar(*, data, subset=None)` `staticmethod`

Array of the left-hand side variables in realized moment conditions.

Parameters:

Name	Type	Description	Default
`data`	`(2, nobs) array`	Returns and realized variance	required
`subset`	`slice`	Which moments to use	`None`

Returns:

Type	Description
`(nobs, 5*nmoms) array`	Dependend variables

`roots(*, param, aggh)`

Roots of the polynomial in moment restrictions.

.. math::

\left(1-A_{2h}^{\sigma}L\right)
\left(1-A_{2h}^{y}L\right)
\left(1-A_{h}^{\sigma}A_{h}^{y}L\right)
\left(1-A_{h}^{y}L\right)
\left(1-A_{h}^{\sigma}L\right)

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`list of floats`

`unc_mean_ct2(param)`

Calculate unconditional second moment of CT, E[y_t**4].

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required

Returns:

Type	Description
`float`

`unc_mean_sigma2(param)`

Calculate unconditional second moment of volatility, E[\sigma_t**4].

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required

Returns:

Type	Description
`float`

`unc_var_ct(param)`

Calculate unconditional variance of CT, V[y_t**2].

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required

Returns:

Type	Description
`float`

`unc_var_error(*, param, aggh)`

Calculate unconditional variance of aggregated volatility error.

:math:V\left[\frac{1}{H}\int_{0}^{H}\epsilon_{t,s}^{\sigma}ds\right].

Derived symbolically in symbolic.py

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required
`aggh`	`float`	Interval length	required

Returns:

Type	Description
`float`

`unc_var_sigma(param)`

Calculate unconditional variance of volatility, V[\sigma_t**2].

Parameters:

Name	Type	Description	Default
`param`	`parameter instance`	Model parameters	required

Returns:

Type	Description
`float`

Model ct

CentTend

__init__(param=None)

coef_big_as(*, param, aggh) staticmethod

coef_big_ay(*, param, aggh) staticmethod

coef_big_bs(*, param, aggh)

coef_big_cs(*, param, aggh)

coef_big_cy(*, param, aggh)

coef_small_as(*, param, aggh)

coef_small_ay(*, param, aggh)

coef_small_bs(*, param, aggh)

coef_small_cs(*, param, aggh)

get_start()

mat_a(*, param, subset=None)

mat_a0(*, param, aggh)

mat_a1(*, param, aggh)

mat_a2(*, param, aggh)

mat_a3(*, param, aggh)

mat_a4(*, param, aggh)

mat_a5(*, param, aggh)

mean_cross(*, param, aggh)

mean_ret(*, param, aggh) staticmethod

mean_vol(*, param, aggh) staticmethod

mean_vol2(*, param, aggh)

realized_const(*, param=None, aggh=1, subset=None)

realized_depvar(*, data, subset=None) staticmethod

roots(*, param, aggh)

unc_mean_ct2(param)

unc_mean_sigma2(param)

unc_var_ct(param)

unc_var_error(*, param, aggh)

unc_var_sigma(param)

`CentTend`

`init(param=None)`

`coef_big_as(*, param, aggh)` `staticmethod`

`coef_big_ay(*, param, aggh)` `staticmethod`

`coef_big_bs(*, param, aggh)`

`coef_big_cs(*, param, aggh)`

`coef_big_cy(*, param, aggh)`

`coef_small_as(*, param, aggh)`

`coef_small_ay(*, param, aggh)`

`coef_small_bs(*, param, aggh)`

`coef_small_cs(*, param, aggh)`

`get_start()`

`mat_a(*, param, subset=None)`

`mat_a0(*, param, aggh)`

`mat_a1(*, param, aggh)`

`mat_a2(*, param, aggh)`

`mat_a3(*, param, aggh)`

`mat_a4(*, param, aggh)`

`mat_a5(*, param, aggh)`

`mean_cross(*, param, aggh)`

`mean_ret(*, param, aggh)` `staticmethod`

`mean_vol(*, param, aggh)` `staticmethod`

`mean_vol2(*, param, aggh)`

`realized_const(*, param=None, aggh=1, subset=None)`

`realized_depvar(*, data, subset=None)` `staticmethod`

`roots(*, param, aggh)`

`unc_mean_ct2(param)`

`unc_mean_sigma2(param)`

`unc_var_ct(param)`

`unc_var_error(*, param, aggh)`

`unc_var_sigma(param)`