def test_targeting(self):
"""Test targeting."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = len(groups)
alpha = [.01, .02, .03, .04, .05, .06]
beta = [.07, .08, .09, .1, .11, .12]
delta = [.13, .14, .15, .16, .17, .18]
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks))
bvecs = np.ones((ncat+1, nstocks))
dvecs = np.ones((ncat+1, nstocks))
avecs[0] = alpha[:4]
avecs[1, :2] *= alpha[-2]
avecs[1, 2:] *= alpha[-1]
bvecs[0] = beta[:4]
bvecs[1, :2] *= beta[-2]
bvecs[1, 2:] *= beta[-1]
dvecs[0] = delta[:4]
dvecs[1, :2] *= delta[-2]
dvecs[1, 2:] *= delta[-1]
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
restriction = 'h**o'
target = param.get_uvar()
param = ParamSpatial.from_abt(avecs=avecs, bvecs=bvecs, groups=groups,
target=target, restriction=restriction,
solve_dvecs=True)
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs,
dvecs=param.dvecs,
groups=groups)
def test_from_abcmat(self):
"""Test spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
weights = ParamSpatial.get_weight(groups)
ncat = 1
alpha, beta, gamma = .01, .16, .09
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha**.5
bvecs = np.ones((ncat+1, nstocks)) * beta**.5
dvecs = np.vstack([np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
amat = np.diag(avecs[0]) + np.diag(avecs[0]).dot(weights[0])
bmat = np.diag(bvecs[0]) + np.diag(bvecs[0]).dot(weights[0])
dmat = np.eye(nstocks) - np.diag(dvecs[1]).dot(weights[0])
dmat_inv = scl.inv(dmat)
cmat = dmat_inv.dot(np.diag(dvecs[0])).dot(dmat_inv)
param = ParamSpatial.from_abcmat(avecs=avecs, bvecs=bvecs, cmat=cmat,
groups=groups)
npt.assert_array_equal(amat, param.amat)
npt.assert_array_equal(bmat, param.bmat)
npt.assert_array_equal(cmat, param.cmat)
npt.assert_array_equal(avecs, param.avecs)
npt.assert_array_equal(bvecs, param.bvecs)
npt.assert_array_equal(None, param.dvecs)
npt.assert_array_equal(weights, param.weights)
def test_from_theta_shomo(self):
"""Test init from theta for spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = len(groups)
alpha, beta, gamma = .01, .16, .09
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha**.5
bvecs = np.ones((ncat+1, nstocks)) * beta**.5
dvecs = np.vstack([np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
restriction = 'shomo'
target = None
theta = [avecs[:, 0], bvecs[:, 0], dvecs[0], dvecs[1:, 0]]
theta = np.concatenate(theta)
param_new = ParamSpatial.from_theta(theta=theta, groups=groups,
restriction=restriction,
target=target)
npt.assert_array_equal(param.amat, param_new.amat)
npt.assert_array_equal(param.bmat, param_new.bmat)
npt.assert_array_equal(param.cmat, param_new.cmat)
npt.assert_array_equal(param.avecs, param_new.avecs)
npt.assert_array_equal(param.bvecs, param_new.bvecs)
npt.assert_array_equal(param.dvecs, param_new.dvecs)
target = param.get_uvar()
theta = [avecs[:, 0], bvecs[:, 0]]
theta = np.concatenate(theta)
cmat = param.find_cmat(amat=param.amat, bmat=param.bmat, target=target)
param_new = ParamSpatial.from_theta(theta=theta, groups=groups,
restriction=restriction,
target=target)
npt.assert_array_equal(param.amat, param_new.amat)
npt.assert_array_equal(param.bmat, param_new.bmat)
npt.assert_array_equal(cmat, param_new.cmat)
npt.assert_array_equal(param.avecs, param_new.avecs)
npt.assert_array_equal(param.bvecs, param_new.bvecs)
# npt.assert_array_equal(None, param_new.dvecs)
cfree = True
theta = [avecs[:, 0], bvecs[:, 0],
param.cmat[np.tril_indices(nstocks)]]
theta = np.concatenate(theta)
param_new = ParamSpatial.from_theta(theta=theta, groups=groups,
restriction=restriction,
cfree=cfree)
npt.assert_array_equal(param.amat, param_new.amat)
npt.assert_array_equal(param.bmat, param_new.bmat)
npt.assert_array_equal(np.tril(param.cmat), param_new.cmat)
npt.assert_array_equal(param.avecs, param_new.avecs)
npt.assert_array_equal(param.bvecs, param_new.bvecs)
npt.assert_array_equal(None, param_new.dvecs)
def test_from_theta_ghomo_special(self):
"""Test group init from theta for spatial specification."""
nstocks = 4
groups = [[(0, 1, 2, 3)]]
ncat = len(groups)
alpha = [.01, .02, .03, .04, .05]
beta = [.07, .08, .09, .1, .11]
delta = [.13, .14, .15, .16, .17]
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks))
bvecs = np.ones((ncat+1, nstocks))
dvecs = np.ones((ncat+1, nstocks))
avecs[0] = alpha[:4]
avecs[1] *= alpha[-1]
bvecs[0] = beta[:4]
bvecs[1] *= beta[-1]
dvecs[0] = delta[:4]
dvecs[1] *= delta[-1]
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
target = param.get_uvar()
theta = np.concatenate([alpha, beta])
cmat = param.find_cmat(amat=param.amat, bmat=param.bmat, target=target)
uvar = param.find_stationary_var(amat=param.amat, bmat=param.bmat,
cmat=cmat)
npt.assert_array_almost_equal(target, uvar)
restriction = 'h**o'
param_homo = ParamSpatial.from_theta(theta=theta, groups=groups,
restriction=restriction,
target=target)
theta_homo = param_homo.get_theta(restriction=restriction,
use_target=False)
restriction = 'ghomo'
param_ghomo = ParamSpatial.from_theta(theta=theta, groups=groups,
restriction=restriction,
target=target)
theta_ghomo = param_ghomo.get_theta(restriction=restriction,
use_target=False)
npt.assert_array_almost_equal(cmat, param.cmat)
npt.assert_array_almost_equal(theta_ghomo, theta_homo, decimal=3)
for param_check in [param_homo, param_ghomo]:
npt.assert_array_equal(param.avecs, param_check.avecs)
npt.assert_array_equal(param.bvecs, param_check.bvecs)
npt.assert_array_equal(param.amat, param_check.amat)
npt.assert_array_equal(param.bmat, param_check.bmat)
npt.assert_array_equal(cmat, param_check.cmat)
def try_interative_estimation_spatial():
"""Try estimating parameters from simple to more complicated model.
"""
restriction = 'full'
nobs = 2000
groups = [[(0, 2), (1, 3)]]
nstocks = np.max(groups) + 1
ncat = len(groups)
alpha = np.array([.1, .01])
beta = np.array([.5, .01])
gamma = .0
# A, B, C - n x n matrices
avecs = np.ones((ncat + 1, nstocks)) * alpha[:, np.newaxis]**.5
bvecs = np.ones((ncat + 1, nstocks)) * beta[:, np.newaxis]**.5
dvecs = np.ones((ncat, nstocks)) * gamma**.5
vvec = np.ones(nstocks)
param_true = ParamSpatial.from_abdv(avecs=avecs,
bvecs=bvecs,
dvecs=dvecs,
vvec=vvec,
groups=groups)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
bekk = BEKK(innov)
result = bekk.estimate(use_target=False,
restriction=restriction,
cfree=False,
model='spatial',
groups=groups)
print(result)
def test_simulation_spatial(self):
"""Test simulation spatial."""
nobs = 10
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = 1
alpha, beta, gamma = .01, .16, .09
# A, B, C - n x n matrices
avecs = np.ones((ncat + 1, nstocks)) * alpha**.5
bvecs = np.ones((ncat + 1, nstocks)) * beta**.5
dvecs = np.vstack(
[np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
param = ParamSpatial.from_abdv(avecs=avecs,
bvecs=bvecs,
dvecs=dvecs,
groups=groups)
for distr in ['normal', 'student', 'skewt']:
innov, hvar = simulate_bekk(param, nobs=nobs, distr=distr)
self.assertEqual(innov.shape, (nobs, nstocks))
self.assertEqual(hvar.shape, (nobs, nstocks, nstocks))
def try_interative_estimation_spatial():
"""Try estimating parameters from simple to more complicated model.
"""
restriction = 'full'
nobs = 2000
groups = [[(0, 2), (1, 3)]]
nstocks = np.max(groups) + 1
ncat = len(groups)
alpha = np.array([.1, .01])
beta = np.array([.5, .01])
gamma = .0
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha[:, np.newaxis]**.5
bvecs = np.ones((ncat+1, nstocks)) * beta[:, np.newaxis]**.5
dvecs = np.ones((ncat, nstocks)) * gamma**.5
vvec = np.ones(nstocks)
param_true = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
vvec=vvec, groups=groups)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
bekk = BEKK(innov)
result = bekk.estimate(use_target=False, restriction=restriction,
cfree=False, model='spatial', groups=groups)
print(result)
def test_from_theta_ghomo(self):
"""Test group init from theta for spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = len(groups)
alpha = [.01, .02, .03, .04, .05, .06]
beta = [.07, .08, .09, .1, .11, .12]
delta = [.13, .14, .15, .16, .17, .18]
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks))
bvecs = np.ones((ncat+1, nstocks))
dvecs = np.ones((ncat+1, nstocks))
avecs[0] = alpha[:4]
avecs[1, :2] *= alpha[-2]
avecs[1, 2:] *= alpha[-1]
bvecs[0] = beta[:4]
bvecs[1, :2] *= beta[-2]
bvecs[1, 2:] *= beta[-1]
dvecs[0] = delta[:4]
dvecs[1, :2] *= delta[-2]
dvecs[1, 2:] *= delta[-1]
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
restriction = 'ghomo'
target = param.get_uvar()
theta = np.concatenate([alpha, beta])
cmat = param.find_cmat(amat=param.amat, bmat=param.bmat, target=target)
uvar = param.find_stationary_var(amat=param.amat, bmat=param.bmat,
cmat=cmat)
npt.assert_array_almost_equal(target, uvar)
param_new = ParamSpatial.from_theta(theta=theta, groups=groups,
restriction=restriction,
target=target)
npt.assert_array_equal(param.avecs, param_new.avecs)
npt.assert_array_equal(param.bvecs, param_new.bvecs)
# npt.assert_array_equal(None, param_new.dvecs)
npt.assert_array_equal(param.amat, param_new.amat)
npt.assert_array_equal(param.bmat, param_new.bmat)
npt.assert_array_equal(cmat, param_new.cmat)
npt.assert_array_almost_equal(cmat, param.cmat)
def try_spatial():
"""Try simulating and estimating spatial BEKK.
"""
cfree = False
restriction = 'h**o'
nobs = 2000
groups = [[(0, 1), (2, 3)]]
nstocks = np.max(groups) + 1
ncat = len(groups)
alpha = np.array([.1, .01])
beta = np.array([.5, .01])
gamma = .09
# A, B, C - n x n matrices
avecs = np.ones((ncat + 1, nstocks)) * alpha[:, np.newaxis]**.5
bvecs = np.ones((ncat + 1, nstocks)) * beta[:, np.newaxis]**.5
dvecs = np.vstack(
[np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
param_true = ParamSpatial.from_abdv(avecs=avecs,
bvecs=bvecs,
dvecs=dvecs,
groups=groups)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
# plot_data(innov, hvar_true)
bekk = BEKK(innov)
for use_target in [True, False]:
result = bekk.estimate(param_start=param_true,
use_target=use_target,
cfree=cfree,
restriction=restriction,
groups=groups,
model='spatial',
method='SLSQP',
cython=True)
print(result)
theta_true = param_true.get_theta(use_target=use_target,
cfree=cfree,
restriction=restriction)
theta_final = result.param_final.get_theta(use_target=use_target,
cfree=cfree,
restriction=restriction)
norm = np.linalg.norm(theta_true - theta_final)
print('\nParameters (true and estimated):')
print(np.vstack([theta_true, theta_final]).T)
print('\nEucledean norm of the difference = %.4f' % norm)
def init_param_spatial(self, restriction='shomo', groups=None,
use_target=False, method='SLSQP', cfree=False,
use_penalty=False):
"""Estimate scalar BEKK with variance targeting.
Parameters
----------
restriction : str
Restriction on parameters.
Must be
- 'hetero' (heterogeneous)
- 'ghomo' (group homogeneous)
- 'h**o' (homogeneous)
- 'shomo' (scalar homogeneous)
cfree : bool
Whether to leave C matrix free (True) or not (False)
groups : list of lists of tuples
Encoded groups of items
method : str
Optimization method. See scipy.optimize.minimize
Returns
-------
ParamSpatial instance
Parameter object
"""
param = ParamSpatial.from_groups(groups=groups,
target=estimate_uvar(self.innov),
abstart=(.2, .7))
if restriction == 'shomo':
return param
kwargs = {'use_target': False, 'groups': groups,
'use_target': use_target,
'use_penalty': use_penalty, 'model': 'spatial',
'cfree': cfree, 'method': method}
est_partial = partial(self.estimate, **kwargs)
if restriction in ('h**o', 'ghomo', 'hetero'):
result = est_partial(param_start=param, restriction='shomo')
param = result.param_final
if restriction in ('ghomo', 'hetero'):
result = est_partial(param_start=param, restriction='h**o')
param = result.param_final
if restriction in ('hetero'):
result = est_partial(param_start=param, restriction='ghomo')
param = result.param_final
return param
def test_init_empty(self):
"""Test spatial specification."""
nstocks = 3
param = ParamSpatial(nstocks=nstocks)
self.assertEqual(param.amat.shape, (nstocks, nstocks))
self.assertEqual(param.bmat.shape, (nstocks, nstocks))
self.assertEqual(param.cmat.shape, (nstocks, nstocks))
self.assertEqual(param.avecs.shape, (2, nstocks))
self.assertEqual(param.bvecs.shape, (2, nstocks))
self.assertEqual(param.dvecs.shape, (2, nstocks))
self.assertEqual(param.weights.shape, (1, nstocks, nstocks))
def test_get_weight(self):
"""Test construction of spatial weights from groups.
"""
groups = [[(0, 1), (2, 3)]]
weight = ParamSpatial.get_weight(groups=groups)
weight_exp = np.zeros((1, 4, 4))
weight_exp[0, 0, 1] = 1
weight_exp[0, 1, 0] = 1
weight_exp[0, 2, 3] = 1
weight_exp[0, 3, 2] = 1
npt.assert_almost_equal(weight, weight_exp)
groups = [[(0, 1, 2)]]
weight = ParamSpatial.get_weight(groups=groups)
weight_exp = np.array([[[0, .5, .5], [.5, 0, .5], [.5, .5, 0]]])
npt.assert_almost_equal(weight, weight_exp)
groups = [[(0, 1), (2, 3)], [(0, 2), (1, 3)]]
weight = ParamSpatial.get_weight(groups=groups)
weight_exp = np.zeros((len(groups), 4, 4))
weight_exp[0, :2, :2] = np.array([[0, 1], [1, 0]])
weight_exp[0, 2:, 2:] = np.array([[0, 1], [1, 0]])
weight_exp[1, 0:3:2, 0:3:2] = np.array([[0, 1], [1, 0]])
weight_exp[1, 1:4:2, 1:4:2] = np.array([[0, 1], [1, 0]])
npt.assert_almost_equal(weight, weight_exp)
groups = [[(0, 1), (2, 3, 4)]]
weight = ParamSpatial.get_weight(groups=groups)
weight_exp = np.zeros((len(groups), 5, 5))
weight_exp[0, :2, :2] = np.array([[0, 1], [1, 0]])
weight_exp[0, 2:, 2:] = np.array([[[0, .5, .5], [.5, 0, .5],
[.5, .5, 0]]])
npt.assert_almost_equal(weight, weight_exp)
def test_get_theta_homo(self):
"""Test theta vector for spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = 1
alpha, beta, gamma = .01, .16, .09
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha**.5
bvecs = np.ones((ncat+1, nstocks)) * beta**.5
dvecs = np.vstack([np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
restriction = 'h**o'
use_target = True
theta = [avecs[0], avecs[1:, 0], bvecs[0], bvecs[1:, 0]]
theta = np.concatenate(theta)
nparams = 2 * (nstocks + ncat)
theta_exp = param.get_theta(restriction=restriction,
use_target=use_target)
self.assertEqual(nparams, theta_exp.size)
self.assertEqual(nparams, theta.size)
npt.assert_array_equal(theta, theta_exp)
use_target = False
theta = [avecs[0], avecs[1:, 0], bvecs[0], bvecs[1:, 0],
dvecs[0], dvecs[1:, 0]]
theta = np.concatenate(theta)
nparams = 3 * (nstocks + ncat)
theta_exp = param.get_theta(restriction=restriction,
use_target=use_target)
self.assertEqual(nparams, theta_exp.size)
self.assertEqual(nparams, theta.size)
npt.assert_array_equal(theta, theta_exp)
cfree = True
theta = [avecs[0], avecs[1:, 0], bvecs[0], bvecs[1:, 0],
param.cmat[np.tril_indices(param.cmat.shape[0])]]
theta = np.concatenate(theta)
nparams = 2 * (nstocks + ncat) + nstocks * (nstocks + 1) // 2
theta_exp = param.get_theta(restriction=restriction, cfree=cfree)
self.assertEqual(nparams, theta_exp.size)
self.assertEqual(nparams, theta.size)
npt.assert_array_equal(theta, theta_exp)
def test_from_abt(self):
"""Test spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
weights = ParamSpatial.get_weight(groups)
ncat = 1
alpha, beta, gamma = .01, .16, .09
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha**.5
bvecs = np.ones((ncat+1, nstocks)) * beta**.5
dvecs = np.vstack([np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
amat = np.diag(avecs[0]) + np.diag(avecs[0]).dot(weights[0])
bmat = np.diag(bvecs[0]) + np.diag(bvecs[0]).dot(weights[0])
dmat = np.eye(nstocks) - np.diag(dvecs[1]).dot(weights[0])
dmat_inv = scl.inv(dmat)
ccmat = dmat_inv.dot(np.diag(dvecs[0])).dot(dmat_inv)
cmat = scl.cholesky(ccmat, 1)
target = ParamSpatial.find_stationary_var(amat=amat, bmat=bmat,
cmat=cmat)
cmat_new = ParamSpatial.find_cmat(amat=amat, bmat=bmat, target=target)
npt.assert_array_almost_equal(cmat[np.tril_indices(nstocks)],
cmat_new[np.tril_indices(nstocks)])
param = ParamSpatial.from_abt(avecs=avecs, bvecs=bvecs, target=target,
groups=groups, restriction='hetero')
npt.assert_array_equal(amat, param.amat)
npt.assert_array_equal(bmat, param.bmat)
npt.assert_array_almost_equal(cmat, param.cmat)
npt.assert_array_equal(avecs, param.avecs)
npt.assert_array_equal(bvecs, param.bvecs)
# npt.assert_array_equal(None, param.dvecs)
npt.assert_array_equal(weights, param.weights)
def try_spatial():
"""Try simulating and estimating spatial BEKK.
"""
cfree = False
restriction = 'h**o'
nobs = 2000
groups = [[(0, 1), (2, 3)]]
nstocks = np.max(groups) + 1
ncat = len(groups)
alpha = np.array([.1, .01])
beta = np.array([.5, .01])
gamma = .09
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha[:, np.newaxis]**.5
bvecs = np.ones((ncat+1, nstocks)) * beta[:, np.newaxis]**.5
dvecs = np.vstack([np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
param_true = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
# plot_data(innov, hvar_true)
bekk = BEKK(innov)
for use_target in [True, False]:
result = bekk.estimate(param_start=param_true, use_target=use_target,
cfree=cfree, restriction=restriction,
groups=groups, model='spatial', method='SLSQP',
cython=True)
print(result)
theta_true = param_true.get_theta(use_target=use_target, cfree=cfree,
restriction=restriction)
theta_final = result.param_final.get_theta(use_target=use_target,
cfree=cfree,
restriction=restriction)
norm = np.linalg.norm(theta_true - theta_final)
print('\nParameters (true and estimated):')
print(np.vstack([theta_true, theta_final]).T)
print('\nEucledean norm of the difference = %.4f' % norm)
def test_get_theta_from_ab(self):
"""Test theta vector for spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = 1
alpha, beta, gamma = .01, .16, .09
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha**.5
bvecs = np.ones((ncat+1, nstocks)) * beta**.5
dvecs = np.vstack([np.ones((1, nstocks)),
np.ones((ncat, nstocks)) * gamma**.5])
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
restriction = 'hetero'
theta = np.concatenate([avecs.flatten(), bvecs.flatten()])
theta_exp = param.get_theta_from_ab(restriction=restriction)
npt.assert_array_equal(theta, theta_exp)
restriction = 'ghomo'
theta = np.concatenate([avecs[0], avecs[1:, :2].flatten(),
bvecs[0], bvecs[1:, :2].flatten()])
theta_exp = param.get_theta_from_ab(restriction=restriction)
npt.assert_array_equal(theta, theta_exp)
restriction = 'h**o'
theta = np.concatenate([avecs[0], avecs[1:, 0],
bvecs[0], bvecs[1:, 0]])
theta_exp = param.get_theta_from_ab(restriction=restriction)
npt.assert_array_equal(theta, theta_exp)
restriction = 'shomo'
theta = np.concatenate([avecs[:, 0], bvecs[:, 0]])
theta_exp = param.get_theta_from_ab(restriction=restriction)
npt.assert_array_equal(theta, theta_exp)
def likelihood(self,
theta,
model='standard',
restriction='full',
target=None,
cfree=False,
groups=None,
cython=True,
use_penalty=False):
"""Compute the conditional log-likelihood function.
Parameters
----------
theta : 1dim array
Dimension depends on the model restriction
model : str
Specific model to estimate.
Must be
- 'standard'
- 'spatial'
restriction : str
Restriction on parameters.
Must be
- 'full'
- 'diagonal'
- 'scalar'
target : (nstocks, nstocks) array
Estimate of unconditional variance matrix
cfree : bool
Whether to leave C matrix free (True) or not (False)
groups : list of lists of tuples
Encoded groups of items
cython : bool
Whether to use Cython optimizations (True) or not (False)
use_penalty : bool
Whether to include penalty term in the likelihood
Returns
-------
float
The value of the minus log-likelihood function.
If some regularity conditions are violated, then it returns
some obscene number.
"""
try:
if model == 'standard':
param = ParamStandard.from_theta(theta=theta,
target=target,
nstocks=self.innov.shape[1],
restriction=restriction)
elif model == 'spatial':
param = ParamSpatial.from_theta(theta=theta,
target=target,
cfree=cfree,
restriction=restriction,
groups=groups)
else:
raise NotImplementedError('The model is not implemented!')
# TODO: Temporary hack to exclude errors in optimization
if isinstance(param, np.ndarray):
return 1e10
if param.constraint() >= 1:
return 1e10
# if param.uvar_bad():
# return 1e10
args = [self.hvar, self.innov, param.amat, param.bmat, param.cmat]
penalty = param.penalty() if use_penalty else 0
if cython:
filter_var(*args)
nstocks = self.innov.shape[1]
idxl = np.tril_indices(nstocks)
idxu = np.triu_indices(nstocks)
self.hvar[:, idxu[0], idxu[1]] = self.hvar[:, idxl[0], idxl[1]]
return likelihood_gauss(self.hvar, self.innov) + penalty
else:
filter_var_python(*args)
return likelihood_python(self.hvar, self.innov) + penalty
except:
return 1e10
def estimate_loop(self,
model='standard',
use_target=True,
groups=None,
restriction='scalar',
cfree=False,
method='SLSQP',
ngrid=2,
use_penalty=False):
"""Estimate parameters starting from a grid of a and b.
Parameters
----------
model : str
Specific model to estimate.
Must be
- 'standard'
- 'spatial'
restriction : str
Restriction on parameters.
Must be
- 'full' = 'diagonal'
- 'group'
- 'scalar'
groups : list of lists of tuples
Encoded groups of items
use_target : bool
Whether to use variance targeting (True) or not (False)
cfree : bool
Whether to leave C matrix free (True) or not (False)
method : str
Optimization method. See scipy.optimize.minimize
ngrid : int
Number of starting values in one dimension
use_penalty : bool
Whether to include penalty term in the likelihood
Returns
-------
BEKKResults instance
Estimation results object
"""
target = estimate_uvar(self.innov)
nstocks = self.innov.shape[1]
achoice = np.linspace(.01, .5, ngrid)
bchoice = np.linspace(.1, .9, ngrid)
out = dict()
for abstart in itertools.product(achoice, bchoice):
if model == 'spatial':
param = ParamSpatial.from_groups(groups=groups,
target=target,
abstart=abstart)
if model == 'standard':
param = ParamStandard(nstocks=nstocks,
target=target,
abstart=abstart)
if param.constraint() >= 1:
continue
result = self.estimate(param_start=param,
method=method,
use_target=use_target,
cfree=cfree,
model=model,
restriction=restriction,
groups=groups,
use_penalty=use_penalty)
out[abstart] = (result.opt_out.fun, result)
df = pd.DataFrame.from_dict(out, orient='index')
return df.sort_values(by=0).iloc[0, 1]
def init_param_spatial(self,
restriction='shomo',
groups=None,
use_target=False,
method='SLSQP',
cfree=False,
use_penalty=False):
"""Estimate scalar BEKK with variance targeting.
Parameters
----------
restriction : str
Restriction on parameters.
Must be
- 'hetero' (heterogeneous)
- 'ghomo' (group homogeneous)
- 'h**o' (homogeneous)
- 'shomo' (scalar homogeneous)
cfree : bool
Whether to leave C matrix free (True) or not (False)
groups : list of lists of tuples
Encoded groups of items
method : str
Optimization method. See scipy.optimize.minimize
Returns
-------
ParamSpatial instance
Parameter object
"""
param = ParamSpatial.from_groups(groups=groups,
target=estimate_uvar(self.innov),
abstart=(.2, .7))
if restriction == 'shomo':
return param
kwargs = {
'use_target': False,
'groups': groups,
'use_target': use_target,
'use_penalty': use_penalty,
'model': 'spatial',
'cfree': cfree,
'method': method
}
est_partial = partial(self.estimate, **kwargs)
if restriction in ('h**o', 'ghomo', 'hetero'):
result = est_partial(param_start=param, restriction='shomo')
param = result.param_final
if restriction in ('ghomo', 'hetero'):
result = est_partial(param_start=param, restriction='h**o')
param = result.param_final
if restriction in ('hetero'):
result = est_partial(param_start=param, restriction='ghomo')
param = result.param_final
return param
def estimate(self,
param_start=None,
restriction='scalar',
cfree=False,
use_target=False,
model='standard',
groups=None,
method='SLSQP',
cython=True,
use_penalty=False):
"""Estimate parameters of the BEKK model.
Parameters
----------
param_start : ParamStandard or ParamSpatial instance
Starting parameters. See Notes for more details.
model : str
Specific model to estimate.
Must be
- 'standard'
- 'spatial'
restriction : str
Restriction on parameters.
Must be
- 'full'
- 'diagonal'
- 'group' (only applicable with 'spatial' model)
- 'scalar'
use_target : bool
Whether to use variance targeting (True) or not (False)
cfree : bool
Whether to leave C matrix free (True) or not (False)
groups : list of lists of tuples
Encoded groups of items
method : str
Optimization method. See scipy.optimize.minimize
cython : bool
Whether to use Cython optimizations (True) or not (False)
use_penalty : bool
Whether to include penalty term in the likelihood
Returns
-------
BEKKResults instance
Estimation results object
Notes
-----
If no param_start is given, the program will estimate parameters in
the order 'from simple to more complicated' (from scalar to diagonal
to full) while always using variance targeting.
"""
# Start timer for the whole optimization
time_start = time.time()
# Check for incompatible inputs
if use_target and cfree:
raise ValueError('use_target and cfree are incompatible!')
# if (groups is not None) and (model != 'spatial'):
# raise ValueError('The model is incompatible with weights!')
# Update default settings
nobs, nstocks = self.innov.shape
var_target = estimate_uvar(self.innov)
self.hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
self.hvar[0] = var_target.copy()
# Check for existence of initial guess among arguments.
# Otherwise, initialize.
if param_start is None:
common = {
'restriction': restriction,
'method': method,
'use_penalty': use_penalty,
'use_target': use_target
}
if model == 'standard':
param_start = self.init_param_standard(**common)
elif model == 'spatial':
param_start = self.init_param_spatial(groups=groups,
cfree=cfree,
**common)
else:
raise NotImplementedError('The model is not implemented!')
# Get vector of parameters to start optimization
theta_start = param_start.get_theta(restriction=restriction,
use_target=use_target,
cfree=cfree)
if use_target:
target = var_target
else:
target = None
# Optimization options
options = {'disp': False, 'maxiter': int(1e6)}
if method == 'Nelder-Mead':
options['maxfev'] = 3000
# Likelihood arguments
kwargs = {
'model': model,
'target': target,
'cfree': cfree,
'restriction': restriction,
'groups': groups,
'cython': cython,
'use_penalty': use_penalty
}
# Likelihood function
likelihood = partial(self.likelihood, **kwargs)
# Run optimization
if method == 'basin':
opt_out = basinhopping(likelihood,
theta_start,
niter=100,
disp=options['disp'],
minimizer_kwargs={'method': 'Nelder-Mead'})
else:
opt_out = minimize(likelihood,
theta_start,
method=method,
options=options)
# How much time did it take in minutes?
time_delta = time.time() - time_start
# Store optimal parameters in the corresponding class
if model == 'standard':
param_final = ParamStandard.from_theta(theta=opt_out.x,
restriction=restriction,
target=target,
nstocks=nstocks)
elif model == 'spatial':
param_final = ParamSpatial.from_theta(theta=opt_out.x,
restriction=restriction,
target=target,
cfree=cfree,
groups=groups)
else:
raise NotImplementedError('The model is not implemented!')
return BEKKResults(innov=self.innov,
hvar=self.hvar,
cython=cython,
var_target=var_target,
model=model,
method=method,
use_target=use_target,
cfree=cfree,
restriction=restriction,
param_start=param_start,
param_final=param_final,
time_delta=time_delta,
opt_out=opt_out)
def try_spatial_combinations():
"""Try simulating spatial BEKK
and estimating it with both spatial and standard.
"""
use_target = False
cfree = True
restriction = 'full'
nstocks = 3
nobs = 2000
groups = [(0, 1)]
weights = ParamSpatial.get_weight(groups=groups, nitems=nstocks)
ncat = weights.shape[0]
alpha = np.array([.1, .01])
beta = np.array([.5, .01])
gamma = .0
# A, B, C - n x n matrices
avecs = np.ones((ncat + 1, nstocks)) * alpha[:, np.newaxis]**.5
bvecs = np.ones((ncat + 1, nstocks)) * beta[:, np.newaxis]**.5
dvecs = np.ones((ncat, nstocks)) * gamma**.5
vvec = np.ones(nstocks)
param_true = ParamSpatial.from_spatial(avecs=avecs,
bvecs=bvecs,
dvecs=dvecs,
vvec=vvec,
weights=weights)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
bekk = BEKK(innov)
# -------------------------------------------------------------------------
# Estimate spatial
result = bekk.estimate(param_start=param_true,
use_target=use_target,
restriction=restriction,
cfree=cfree,
model='spatial',
weights=weights,
method='SLSQP',
cython=True)
print(result)
theta_true = param_true.get_theta(use_target=use_target,
cfree=cfree,
restriction=restriction)
theta_final = result.param_final.get_theta(use_target=use_target,
cfree=cfree,
restriction=restriction)
norm = np.linalg.norm(theta_true - theta_final)
print('\nParameters (true and estimated):\n',
np.vstack([theta_true, theta_final]).T)
print('\nEucledean norm of the difference = %.4f' % norm)
# -------------------------------------------------------------------------
# Estimate standard
param_true = ParamStandard.from_abc(amat=param_true.amat,
bmat=param_true.bmat,
cmat=param_true.cmat)
result = bekk.estimate(param_start=param_true,
use_target=use_target,
restriction=restriction,
cfree=cfree,
model='standard',
weights=weights,
method='SLSQP',
cython=True)
print(result)
theta_true = param_true.get_theta(use_target=use_target,
restriction=restriction)
theta_final = result.param_final.get_theta(use_target=use_target,
restriction=restriction)
norm = np.linalg.norm(theta_true - theta_final)
print('\nParameters (true and estimated):\n',
np.vstack([theta_true, theta_final]).T)
print('\nEucledean norm of the difference = %.4f' % norm)
def estimate(self, param_start=None, restriction='scalar', cfree=False,
use_target=False, model='standard', groups=None,
method='SLSQP', cython=True, use_penalty=False):
"""Estimate parameters of the BEKK model.
Parameters
----------
param_start : ParamStandard or ParamSpatial instance
Starting parameters. See Notes for more details.
model : str
Specific model to estimate.
Must be
- 'standard'
- 'spatial'
restriction : str
Restriction on parameters.
Must be
- 'full'
- 'diagonal'
- 'group' (only applicable with 'spatial' model)
- 'scalar'
use_target : bool
Whether to use variance targeting (True) or not (False)
cfree : bool
Whether to leave C matrix free (True) or not (False)
groups : list of lists of tuples
Encoded groups of items
method : str
Optimization method. See scipy.optimize.minimize
cython : bool
Whether to use Cython optimizations (True) or not (False)
use_penalty : bool
Whether to include penalty term in the likelihood
Returns
-------
BEKKResults instance
Estimation results object
Notes
-----
If no param_start is given, the program will estimate parameters in
the order 'from simple to more complicated' (from scalar to diagonal
to full) while always using variance targeting.
"""
# Start timer for the whole optimization
time_start = time.time()
# Check for incompatible inputs
if use_target and cfree:
raise ValueError('use_target and cfree are incompatible!')
# if (groups is not None) and (model != 'spatial'):
# raise ValueError('The model is incompatible with weights!')
# Update default settings
nobs, nstocks = self.innov.shape
var_target = estimate_uvar(self.innov)
self.hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
self.hvar[0] = var_target.copy()
# Check for existence of initial guess among arguments.
# Otherwise, initialize.
if param_start is None:
common = {'restriction': restriction, 'method': method,
'use_penalty': use_penalty, 'use_target': use_target}
if model == 'standard':
param_start = self.init_param_standard(**common)
elif model == 'spatial':
param_start = self.init_param_spatial(groups=groups,
cfree=cfree, **common)
else:
raise NotImplementedError('The model is not implemented!')
# Get vector of parameters to start optimization
theta_start = param_start.get_theta(restriction=restriction,
use_target=use_target, cfree=cfree)
if use_target:
target = var_target
else:
target = None
# Optimization options
options = {'disp': False, 'maxiter': int(1e6)}
if method == 'Nelder-Mead':
options['maxfev'] = 3000
# Likelihood arguments
kwargs = {'model': model, 'target': target, 'cfree': cfree,
'restriction': restriction, 'groups': groups,
'cython': cython, 'use_penalty': use_penalty}
# Likelihood function
likelihood = partial(self.likelihood, **kwargs)
# Run optimization
if method == 'basin':
opt_out = basinhopping(likelihood, theta_start, niter=100,
disp=options['disp'],
minimizer_kwargs={'method': 'Nelder-Mead'})
else:
opt_out = minimize(likelihood, theta_start,
method=method, options=options)
# How much time did it take in minutes?
time_delta = time.time() - time_start
# Store optimal parameters in the corresponding class
if model == 'standard':
param_final = ParamStandard.from_theta(theta=opt_out.x,
restriction=restriction,
target=target,
nstocks=nstocks)
elif model == 'spatial':
param_final = ParamSpatial.from_theta(theta=opt_out.x,
restriction=restriction,
target=target, cfree=cfree,
groups=groups)
else:
raise NotImplementedError('The model is not implemented!')
return BEKKResults(innov=self.innov, hvar=self.hvar, cython=cython,
var_target=var_target, model=model, method=method,
use_target=use_target, cfree=cfree,
restriction=restriction,
param_start=param_start, param_final=param_final,
time_delta=time_delta, opt_out=opt_out)
def estimate_loop(self, model='standard', use_target=True, groups=None,
restriction='scalar', cfree=False,
method='SLSQP', ngrid=2, use_penalty=False):
"""Estimate parameters starting from a grid of a and b.
Parameters
----------
model : str
Specific model to estimate.
Must be
- 'standard'
- 'spatial'
restriction : str
Restriction on parameters.
Must be
- 'full' = 'diagonal'
- 'group'
- 'scalar'
groups : list of lists of tuples
Encoded groups of items
use_target : bool
Whether to use variance targeting (True) or not (False)
cfree : bool
Whether to leave C matrix free (True) or not (False)
method : str
Optimization method. See scipy.optimize.minimize
ngrid : int
Number of starting values in one dimension
use_penalty : bool
Whether to include penalty term in the likelihood
Returns
-------
BEKKResults instance
Estimation results object
"""
target = estimate_uvar(self.innov)
nstocks = self.innov.shape[1]
achoice = np.linspace(.01, .5, ngrid)
bchoice = np.linspace(.1, .9, ngrid)
out = dict()
for abstart in itertools.product(achoice, bchoice):
if model == 'spatial':
param = ParamSpatial.from_groups(groups=groups,
target=target,
abstart=abstart)
if model == 'standard':
param = ParamStandard(nstocks=nstocks, target=target,
abstart=abstart)
if param.constraint() >= 1:
continue
result = self.estimate(param_start=param, method=method,
use_target=use_target, cfree=cfree,
model=model, restriction=restriction,
groups=groups, use_penalty=use_penalty)
out[abstart] = (result.opt_out.fun, result)
df = pd.DataFrame.from_dict(out, orient='index')
return df.sort_values(by=0).iloc[0, 1]
def likelihood(self, theta, model='standard', restriction='full',
target=None, cfree=False, groups=None, cython=True,
use_penalty=False):
"""Compute the conditional log-likelihood function.
Parameters
----------
theta : 1dim array
Dimension depends on the model restriction
model : str
Specific model to estimate.
Must be
- 'standard'
- 'spatial'
restriction : str
Restriction on parameters.
Must be
- 'full'
- 'diagonal'
- 'scalar'
target : (nstocks, nstocks) array
Estimate of unconditional variance matrix
cfree : bool
Whether to leave C matrix free (True) or not (False)
groups : list of lists of tuples
Encoded groups of items
cython : bool
Whether to use Cython optimizations (True) or not (False)
use_penalty : bool
Whether to include penalty term in the likelihood
Returns
-------
float
The value of the minus log-likelihood function.
If some regularity conditions are violated, then it returns
some obscene number.
"""
try:
if model == 'standard':
param = ParamStandard.from_theta(theta=theta, target=target,
nstocks=self.innov.shape[1],
restriction=restriction)
elif model == 'spatial':
param = ParamSpatial.from_theta(theta=theta, target=target,
cfree=cfree,
restriction=restriction,
groups=groups)
else:
raise NotImplementedError('The model is not implemented!')
# TODO: Temporary hack to exclude errors in optimization
if isinstance(param, np.ndarray):
return 1e10
if param.constraint() >= 1:
return 1e10
# if param.uvar_bad():
# return 1e10
args = [self.hvar, self.innov, param.amat, param.bmat, param.cmat]
penalty = param.penalty() if use_penalty else 0
if cython:
filter_var(*args)
nstocks = self.innov.shape[1]
idxl = np.tril_indices(nstocks)
idxu = np.triu_indices(nstocks)
self.hvar[:, idxu[0], idxu[1]] = self.hvar[:, idxl[0], idxl[1]]
return likelihood_gauss(self.hvar, self.innov) + penalty
else:
filter_var_python(*args)
return likelihood_python(self.hvar, self.innov) + penalty
except:
return 1e10
def try_spatial_combinations():
"""Try simulating spatial BEKK
and estimating it with both spatial and standard.
"""
use_target = False
cfree = True
restriction = 'full'
nstocks = 3
nobs = 2000
groups = [(0, 1)]
weights = ParamSpatial.get_weight(groups=groups, nitems=nstocks)
ncat = weights.shape[0]
alpha = np.array([.1, .01])
beta = np.array([.5, .01])
gamma = .0
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks)) * alpha[:, np.newaxis]**.5
bvecs = np.ones((ncat+1, nstocks)) * beta[:, np.newaxis]**.5
dvecs = np.ones((ncat, nstocks)) * gamma**.5
vvec = np.ones(nstocks)
param_true = ParamSpatial.from_spatial(avecs=avecs, bvecs=bvecs,
dvecs=dvecs, vvec=vvec,
weights=weights)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
bekk = BEKK(innov)
# -------------------------------------------------------------------------
# Estimate spatial
result = bekk.estimate(param_start=param_true, use_target=use_target,
restriction=restriction, cfree=cfree,
model='spatial', weights=weights, method='SLSQP',
cython=True)
print(result)
theta_true = param_true.get_theta(use_target=use_target, cfree=cfree,
restriction=restriction)
theta_final = result.param_final.get_theta(use_target=use_target,
cfree=cfree,
restriction=restriction)
norm = np.linalg.norm(theta_true - theta_final)
print('\nParameters (true and estimated):\n',
np.vstack([theta_true, theta_final]).T)
print('\nEucledean norm of the difference = %.4f' % norm)
# -------------------------------------------------------------------------
# Estimate standard
param_true = ParamStandard.from_abc(amat=param_true.amat,
bmat=param_true.bmat,
cmat=param_true.cmat)
result = bekk.estimate(param_start=param_true, use_target=use_target,
restriction=restriction, cfree=cfree,
model='standard', weights=weights, method='SLSQP',
cython=True)
print(result)
theta_true = param_true.get_theta(use_target=use_target,
restriction=restriction)
theta_final = result.param_final.get_theta(use_target=use_target,
restriction=restriction)
norm = np.linalg.norm(theta_true - theta_final)
print('\nParameters (true and estimated):\n',
np.vstack([theta_true, theta_final]).T)
print('\nEucledean norm of the difference = %.4f' % norm)
def test_get_theta_ghomo(self):
"""Test theta vector for spatial specification."""
nstocks = 4
groups = [[(0, 1), (2, 3)]]
ncat = len(groups)
alpha = [.01, .02, .03]
beta = [.04, .05, .06]
delta = [.07, .08]
# A, B, C - n x n matrices
avecs = np.ones((ncat+1, nstocks))
bvecs = np.ones((ncat+1, nstocks))
dvecs = np.ones((ncat+1, nstocks))
avecs[0, :] *= alpha[0]
avecs[1, :2] *= alpha[1]
avecs[1, 2:] *= alpha[2]
bvecs[0, :] *= beta[0]
bvecs[1, :2] *= beta[1]
bvecs[1, 2:] *= beta[2]
dvecs[1, :2] *= delta[0]
dvecs[1, 2:] *= delta[1]
param = ParamSpatial.from_abdv(avecs=avecs, bvecs=bvecs, dvecs=dvecs,
groups=groups)
restriction = 'ghomo'
use_target = True
theta = [avecs[0], [avecs[1, 0]], [avecs[1, 2]],
bvecs[0], [bvecs[1, 0]], [bvecs[1, 2]]]
theta = np.concatenate(theta)
nparams = 2 * (nstocks + 2 * ncat)
theta_exp = param.get_theta(restriction=restriction,
use_target=use_target)
self.assertEqual(nparams, theta_exp.size)
self.assertEqual(nparams, theta.size)
npt.assert_array_equal(theta, theta_exp)
use_target = False
theta = [avecs[0], [avecs[1, 0]], [avecs[1, 2]],
bvecs[0], [bvecs[1, 0]], [bvecs[1, 2]],
dvecs[0], [dvecs[1, 0]], [dvecs[1, 2]]]
theta = np.concatenate(theta)
nparams = 3 * (nstocks + 2 * ncat)
theta_exp = param.get_theta(restriction=restriction,
use_target=use_target)
self.assertEqual(nparams, theta_exp.size)
self.assertEqual(nparams, theta.size)
npt.assert_array_equal(theta, theta_exp)
cfree = True
theta = [avecs[0], [avecs[1, 0]], [avecs[1, 2]],
bvecs[0], [bvecs[1, 0]], [bvecs[1, 2]],
param.cmat[np.tril_indices(param.cmat.shape[0])]]
theta = np.concatenate(theta)
nparams = 2 * (nstocks + 2 * ncat) + nstocks * (nstocks + 1) // 2
theta_exp = param.get_theta(restriction=restriction, cfree=cfree)
self.assertEqual(nparams, theta_exp.size)
self.assertEqual(nparams, theta.size)
npt.assert_array_equal(theta, theta_exp)