Parameter classes¶

Generic parameter class¶

class bekk.param_generic.ParamGeneric(nstocks=2, abstart=(0.1, 0.85), target=None)[source]¶

Class to hold parameters of the BEKK model.

Attributes

amat, bmat, cmat

Matrix representations of BEKK parameters

Methods

`from_abc`([amat, bmat, cmat])	Initialize from A, B, and C arrays.
`find_cmat`([amat, bmat, ccmat, target])	Find C matrix given A, B, and H.
`from_target`([amat, bmat, target])	Initialize from A, B, and variance target.
`find_stationary_var`([amat, bmat, cmat])	Find fixed point of H = CC’ + AHA’ + BHB’ given A, B, C.
`get_uvar`()	Unconditional variance matrix regardless of the model.
`constraint`()	Compute the largest eigenvalue of BEKK model.

constraint()[source]¶

Compute the largest eigenvalue of BEKK model.

Returns:

float

Largest eigenvalue

static find_ccmat(amat=None, bmat=None, target=None)[source]¶

Find CC’ matrix given A, B, and H in H = CC’ + AHA’ + BHB’ given A, B, H.

Parameters:

amat, bmat, target : (nstocks, nstocks) arrays

Parameter matrices

Returns:

(nstocks, nstocks) array

static find_cmat(amat=None, bmat=None, ccmat=None, target=None)[source]¶

Find C matrix given A, B, and H. Solve for C in H = CC’ + AHA’ + BHB’ given A, B, H.

Parameters:

amat, bmat, target : (nstocks, nstocks) arrays

Parameter matrices

Returns:

(nstocks, nstocks) array

Cholesky decomposition of CC’

static find_stationary_var(amat=None, bmat=None, cmat=None)[source]¶

Find fixed point of H = CC’ + AHA’ + BHB’ given A, B, C.

Parameters:

amat, bmat, cmat : (nstocks, nstocks) arrays

Parameter matrices

Returns:

(nstocks, nstocks) array

Unconditional variance matrix

static fixed_point(uvar, amat=None, bmat=None, ccmat=None)[source]¶

Function for finding fixed point of H = CC’ + AHA’ + BHB’ given A, B, C.

Parameters:

uvar : 1d array

Lower triangle of symmetric variance matrix

amat, bmat, ccmat : (nstocks, nstocks) arrays

Parameter matrices

Returns:

(nstocks, nstocks) array

classmethod from_abc(amat=None, bmat=None, cmat=None)[source]¶

Initialize from A, B, and C arrays.

Parameters:

amat, bmat, cmat : (nstocks, nstocks) arrays

Parameter matrices

Returns:

param : BEKKParams instance

BEKK parameters

classmethod from_target(amat=None, bmat=None, target=None)[source]¶

Initialize from A, B, and variance target.

Parameters:

amat, bmat, target : (nstocks, nstocks) arrays

Parameter matrices

Returns:

param : BEKKParams instance

BEKK parameters

get_uvar()[source]¶

Unconditional variance matrix regardless of the model.

Returns:

(nstocks, nstocks) array

Unconditional variance amtrix

penalty()[source]¶: Penalty in the likelihood for bad parameter values.

uvar_bad()[source]¶: Check that unconditional variance is well defined.

Standadrd parameter class¶

class bekk.param_standard.ParamStandard(nstocks=2, abstart=(0.1, 0.6), target=None)[source]¶

Class to hold parameters of the BEKK model.

Attributes

amat, bmat, cmat

Matrix representations of BEKK parameters

Methods

`from_theta`([theta, nstocks, cfree, …])	Initialize from theta vector.
`get_theta`([restriction, use_target, cfree])	Convert parameter mratrices to 1-dimensional array.

classmethod from_theta(theta=None, nstocks=None, cfree=True, restriction='scalar', target=None)[source]¶

Initialize from theta vector.

Parameters:

theta : 1d array

Length depends on the model restrictions and variance targeting

If target is not None:

‘full’ - 2*n**2

‘diagonal’ - 2*n

‘scalar’ - 2

If target is None:

+(n+1)*n/2 for parameter C

nstocks : int

Number of stocks in the model

restriction : str

Can be

‘full’

‘diagonal’

‘scalar’

target : (nstocks, nstocks) array

Variance target matrix

Returns:

param : BEKKParams instance

BEKK parameters

get_theta(restriction='scalar', use_target=True, cfree=True)[source]¶

Convert parameter mratrices to 1-dimensional array.

Parameters:

restriction : str

Can be

‘full’

‘diagonal’

‘scalar’

use_target : bool

Whether to estimate only A and B (True) or C as well (False)

Returns:

theta : 1d array

Length depends on the model restrictions and variance targeting

If use_target is True:

‘full’ - 2*n**2

‘diagonal’ - 2*n

‘scalar’ - 2

If use_target is False:

+(n+1)*n/2 for parameter cmat

Spatial parameter class¶

class bekk.param_spatial.ParamSpatial(nstocks=2)[source]¶

Class to hold parameters of the BEKK model.

Attributes

amat, bmat, cmat, avecs, bvecs, dvecs	Matrix representations of BEKK parameters
groups	List of related items
weights	Spatial relation matrices

Methods

`from_theta`([theta, groups, cfree, …])	Initialize from theta vector.
`get_theta`([restriction, use_target, cfree])	Convert parameter matrices to 1-dimensional array.
`get_weight`([groups])	Generate weighting matrices given groups.

classmethod from_theta(theta=None, groups=None, cfree=False, restriction='shomo', target=None, solve_dvecs=False)[source]¶

Initialize from theta vector.

Parameters:

theta : 1d array

Length depends on the model restrictions and variance targeting

weights : (ncat, nstocks, nstocks) array

Weight matrices

groups : list of lists of tuples

Encoded groups of items

cfree : bool

Whether to leave C matrix free (True) or not (False)

target : (nstocks, nstocks) array

Variance target matrix

restriction : str

Can be

‘hetero’ (heterogeneous)

‘ghomo’ (group homogeneous)

‘homo’ (homogeneous)

‘shomo’ (scalar homogeneous)

Returns:

param : BEKKParams instance

BEKK parameters

get_theta(restriction='shomo', use_target=False, cfree=False)[source]¶

Convert parameter matrices to 1-dimensional array.

Parameters:

restriction : str

Can be

‘hetero’ (heterogeneous)

‘ghomo’ (group homogeneous)

‘homo’ (homogeneous)

‘shomo’ (scalar homogeneous)

use_target : bool

Whether to estimate only A and B (True) or C as well (False)

cfree : bool

Whether to leave C matrix free (True) or not (False)

Returns:

theta : 1d array

Length depends on the model restrictions and variance targeting

If use_target is True:

‘hetero’ - 2*n*(m+1)

‘ghomo’ - 2*(n+m*k)

‘homo’ - 2*(n+m)

‘shomo’ - 2*(m+1)

If use_target is False and cfree is False:

‘hetero’ - +n*(m+1)

‘ghomo’ - +(n+m*k)

‘homo’ - +(n+m)

‘shomo’ - +(n+m)

If use_target is False and cfree is True:

+n*(n+1)/2

static get_weight(groups=None)[source]¶

Generate weighting matrices given groups.

Parameters:

groups : list of lists of tuples

Encoded groups of items

Returns:

(ngroups, nitems, nitems) array

Spatial weights

Examples

>>> print(ParamSpatial.get_weight(groups=[[(0, 1)]]))
[[[ 0.  1.]
  [ 1.  0.]]]
>>> print(ParamSpatial.get_weight(groups=[[(0, 1, 2)]]))
[[[ 0.   0.5  0.5]
  [ 0.5  0.   0.5]
  [ 0.5  0.5  0. ]]]
>>> print(ParamSpatial.get_weight(groups=[[(0, 1), (2, 3)]]))
[[[ 0.  1.  0.  0.]
  [ 1.  0.  0.  0.]
  [ 0.  0.  0.  1.]
  [ 0.  0.  1.  0.]]]
>>> print(ParamSpatial.get_weight(groups=[[(0, 1), (2, 3, 4)]]))
[[[ 0.   1.   0.   0.   0. ]
  [ 1.   0.   0.   0.   0. ]
  [ 0.   0.   0.   0.5  0.5]
  [ 0.   0.   0.5  0.   0.5]
  [ 0.   0.   0.5  0.5  0. ]]]