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_weights(self):
"""Test weighting function.
"""
nstocks = 6
nobs = 10
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
innov, hvar = simulate_bekk(param, nobs=nobs)
res = BEKKResults(innov=innov, hvar=hvar)
weights = res.weights()
npt.assert_array_equal(weights, np.ones_like(innov) / nstocks)
weights = res.weights(kind='equal')
npt.assert_array_equal(weights, np.ones_like(innov) / nstocks)
weights = res.weights(kind='minvar')
for hvari, wi in zip(hvar, weights):
hinv = np.linalg.solve(hvari, np.ones(nstocks))
npt.assert_array_almost_equal(wi, hinv / hinv.sum())
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_standard():
"""Try simulating and estimating standard BEKK.
"""
use_target = False
restriction = 'full'
nstocks = 6
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
# plot_data(innov, hvar_true)
bekk = BEKK(innov)
result = bekk.estimate(param_start=param_true, use_target=use_target,
model='standard', method='SLSQP',
restriction=restriction)
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 try_bekk():
"""Simulate and estimate BEKK model.
"""
nstocks = 2
use_target = True
nobs = 2000
restriction = 'full'
simulate = True
# A, B, C - n x n matrices
A = np.eye(nstocks) * .09**.5
B = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=A, bmat=B, target=target)
theta_true = param_true.get_theta(use_target=use_target,
restriction=restriction)
print('True parameter:\n', theta_true)
# Data file
innov_file = '../data/innovations.npy'
if simulate:
# Simulate data
innov, hvar_true = simulate_bekk(param_true,
nobs=nobs,
distr='skewt',
degf=30)
np.savetxt(innov_file[:-4] + '.csv', innov, delimiter=",")
else:
# Regenerate real data
download_data(innov_file=innov_file, nstocks=nstocks, nobs=nobs)
# Load data from the drive
innov = np.load(innov_file)
# Estimate parameters
params = []
for cython in [True, False]:
time_start = time.time()
# Initialize the object
bekk = BEKK(innov)
bekk.estimate(param_start=param_true,
restriction=restriction,
use_target=use_target,
method='SLSQP',
cython=cython)
print('Cython: ', cython)
theta_final = bekk.param_final.get_theta(restriction=restriction,
use_target=use_target)
print(theta_final)
params.append(theta_final)
print('Time elapsed %.2f, seconds\n' % (time.time() - time_start))
print('\nNorm difference between the estimates: %.4f' %
np.linalg.norm(params[0] - params[1]))
return bekk
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 try_bekk():
"""Simulate and estimate BEKK model.
"""
nstocks = 2
use_target = True
nobs = 2000
restriction = 'full'
simulate = True
# A, B, C - n x n matrices
A = np.eye(nstocks) * .09**.5
B = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=A, bmat=B, target=target)
theta_true = param_true.get_theta(use_target=use_target,
restriction=restriction)
print('True parameter:\n', theta_true)
# Data file
innov_file = '../data/innovations.npy'
if simulate:
# Simulate data
innov, hvar_true = simulate_bekk(param_true, nobs=nobs,
distr='skewt', degf=30)
np.savetxt(innov_file[:-4] + '.csv', innov, delimiter=",")
else:
# Regenerate real data
download_data(innov_file=innov_file, nstocks=nstocks, nobs=nobs)
# Load data from the drive
innov = np.load(innov_file)
# Estimate parameters
params = []
for cython in [True, False]:
time_start = time.time()
# Initialize the object
bekk = BEKK(innov)
bekk.estimate(param_start=param_true, restriction=restriction,
use_target=use_target, method='SLSQP', cython=cython)
print('Cython: ', cython)
theta_final = bekk.param_final.get_theta(restriction=restriction,
use_target=use_target)
print(theta_final)
params.append(theta_final)
print('Time elapsed %.2f, seconds\n' % (time.time() - time_start))
print('\nNorm difference between the estimates: %.4f'
% np.linalg.norm(params[0] - params[1]))
return bekk
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_simulation(self):
"""Test simulation."""
nstocks = 6
nobs = 10
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
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_iterative_estimation_standard():
"""Try estimating parameters from simple to more complicated model.
"""
restriction = 'scalar'
nstocks = 3
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
bekk = BEKK(innov)
result = bekk.estimate(use_target=False, restriction=restriction)
print(result)
def try_standard_loss():
"""Try forecast evaluation of BEKK model.
"""
model = 'standard'
use_target = True
nstocks = 2
nobs = 1000
window = 990
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
kwargs = {
'param_start': param_true,
'innov_all': innov,
'window': window,
'model': model,
'use_target': use_target,
'alpha': .25,
'kind': 'equal'
}
evaluate = partial(BEKK.collect_losses, **kwargs)
losses = []
restrcs = ['scalar', 'diagonal', 'full']
for restr in restrcs:
losses.append(evaluate(restriction=restr))
losses = pd.concat(losses)
print(losses)
df = losses['qlike'].unstack('restriction')
mcs = MCS(df, size=.1)
mcs.compute()
print(mcs.pvalues)
return losses
def try_iterative_estimation_standard():
"""Try estimating parameters from simple to more complicated model.
"""
restriction = 'scalar'
nstocks = 3
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
bekk = BEKK(innov)
result = bekk.estimate(use_target=False, restriction=restriction)
print(result)
def test_likelihood(self):
"""Test likelihood."""
nstocks = 2
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
innov, hvar = simulate_bekk(param, nobs=nobs, distr='normal')
out1 = likelihood_python(hvar, innov)
out2 = likelihood_gauss(hvar, innov)
self.assertIsInstance(out1, float)
self.assertIsInstance(out2, float)
self.assertAlmostEqual(out1, out2)
def time_likelihood():
"""Compare speeds of recrsions and likelihoods.
"""
nstocks = 2
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
cmat = param_true.cmat
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
hvar[0] = param_true.get_uvar().copy()
with take_time('Python recursion'):
filter_var_python(hvar, innov, amat, bmat, cmat)
hvar1 = hvar.copy()
hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
hvar[0] = param_true.get_uvar().copy()
with take_time('Cython recursion'):
filter_var(hvar, innov, amat, bmat, cmat)
hvar2 = hvar.copy()
idxl = np.tril_indices(nstocks)
idxu = np.triu_indices(nstocks)
hvar2[:, idxu[0], idxu[1]] = hvar2[:, idxl[0], idxl[1]]
print(np.allclose(hvar_true, hvar1))
print(np.allclose(hvar_true, hvar2))
with take_time('Python likelihood'):
out1 = likelihood_python(hvar, innov)
with take_time('Cython likelihood'):
out2 = likelihood_gauss(hvar, innov)
print(np.allclose(out1, out2))
def time_likelihood():
"""Compare speeds of recrsions and likelihoods.
"""
nstocks = 2
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
cmat = param_true.cmat
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
hvar[0] = param_true.get_uvar().copy()
with take_time('Python recursion'):
filter_var_python(hvar, innov, amat, bmat, cmat)
hvar1 = hvar.copy()
hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
hvar[0] = param_true.get_uvar().copy()
with take_time('Cython recursion'):
filter_var(hvar, innov, amat, bmat, cmat)
hvar2 = hvar.copy()
idxl = np.tril_indices(nstocks)
idxu = np.triu_indices(nstocks)
hvar2[:, idxu[0], idxu[1]] = hvar2[:, idxl[0], idxl[1]]
print(np.allclose(hvar_true, hvar1))
print(np.allclose(hvar_true, hvar2))
with take_time('Python likelihood'):
out1 = likelihood_python(hvar, innov)
with take_time('Cython likelihood'):
out2 = likelihood_gauss(hvar, innov)
print(np.allclose(out1, out2))
def test_filter_var(self):
"""Test recursions."""
nstocks = 2
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
cmat = param.cmat
innov, hvar_true = simulate_bekk(param, nobs=nobs, distr='normal')
hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
hvar[0] = param.get_uvar()
out1 = filter_var_python(hvar, innov, amat, bmat, cmat)
hvar = np.zeros((nobs, nstocks, nstocks), dtype=float)
hvar[0] = param.get_uvar()
out2 = filter_var(hvar, innov, amat, bmat, cmat)
idxl = np.tril_indices(nstocks)
idxu = np.triu_indices(nstocks)
npt.assert_array_almost_equal(hvar_true,
np.transpose(hvar_true, axes=(0, 2, 1)))
# npt.assert_array_almost_equal(out2, np.transpose(out2, axes=(0, 2, 1)))
out2[:, idxu[0], idxu[1]] = out2[:, idxl[0], idxl[1]]
npt.assert_array_almost_equal(out1, np.transpose(out1, axes=(0, 2, 1)))
npt.assert_array_almost_equal(out2, np.transpose(out2, axes=(0, 2, 1)))
npt.assert_array_almost_equal(hvar_true, out1)
npt.assert_array_almost_equal(hvar_true, out2)
def try_standard_loss():
"""Try forecast evaluation of BEKK model.
"""
model = 'standard'
use_target = True
nstocks = 2
nobs = 1000
window = 990
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
kwargs = {'param_start': param_true, 'innov_all': innov,
'window': window, 'model': model, 'use_target': use_target,
'alpha': .25, 'kind': 'equal'}
evaluate = partial(BEKK.collect_losses, **kwargs)
losses = []
restrcs = ['scalar', 'diagonal', 'full']
for restr in restrcs:
losses.append(evaluate(restriction=restr))
losses = pd.concat(losses)
print(losses)
df = losses['qlike'].unstack('restriction')
mcs = MCS(df, size=.1)
mcs.compute()
print(mcs.pvalues)
return losses
def try_standard():
"""Try simulating and estimating standard BEKK.
"""
use_target = False
restriction = 'full'
nstocks = 6
nobs = 2000
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param_true = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
print(param_true)
innov, hvar_true = simulate_bekk(param_true, nobs=nobs, distr='normal')
# plot_data(innov, hvar_true)
bekk = BEKK(innov)
result = bekk.estimate(param_start=param_true,
use_target=use_target,
model='standard',
method='SLSQP',
restriction=restriction)
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_var_ratio(self):
"""Test variance ratio."""
nstocks = 6
nobs = 10
# A, B, C - n x n matrices
amat = np.eye(nstocks) * .09**.5
bmat = np.eye(nstocks) * .9**.5
target = np.eye(nstocks)
param = ParamStandard.from_target(amat=amat, bmat=bmat, target=target)
innov, hvar = simulate_bekk(param, nobs=nobs)
res = BEKKResults(innov=innov, hvar=hvar)
evar = res.portf_evar()
rvar = res.portf_rvar()
vratio = res.loss_var_ratio()
mvar = res.portf_mvar()
self.assertEqual(evar.shape, (nobs, ))
self.assertEqual(rvar.shape, (nobs, ))
self.assertEqual(vratio.shape, (nobs, ))
self.assertIsInstance(mvar, float)
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 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)
