def test_cases(self):
# Test against known results
for unconstrained, error_variance, constrained in self.cases:
result = tools.constrain_stationary_multivariate(
unconstrained, error_variance)
assert_allclose(result[0], constrained)
# Test that the constrained results correspond to companion matrices
# with eigenvalues less than 1 in modulus
for unconstrained in self.eigval_cases:
if type(unconstrained) == list:
cov = np.eye(unconstrained[0].shape[0])
else:
cov = np.eye(unconstrained.shape[0])
constrained, _ = tools.constrain_stationary_multivariate(unconstrained, cov)
companion = tools.companion_matrix(
[1] + [-constrained[i] for i in range(len(constrained))]
).T
assert_equal(np.max(np.abs(np.linalg.eigvals(companion))) < 1, True)
def test_cases(self):
for constrained in self.constrained_cases:
if type(constrained) == list:
cov = np.eye(constrained[0].shape[0])
else:
cov = np.eye(constrained.shape[0])
unconstrained, _ = tools.unconstrain_stationary_multivariate(constrained, cov)
reconstrained, _ = tools.constrain_stationary_multivariate(unconstrained, cov)
assert_allclose(reconstrained, constrained)
for unconstrained in self.unconstrained_cases:
if type(unconstrained) == list:
cov = np.eye(unconstrained[0].shape[0])
else:
cov = np.eye(unconstrained.shape[0])
constrained, _ = tools.constrain_stationary_multivariate(unconstrained, cov)
reunconstrained, _ = tools.unconstrain_stationary_multivariate(constrained, cov)
# Note: low tolerance comes from last example in unconstrained_cases,
# but is not a real problem
assert_allclose(reunconstrained, unconstrained, atol=1e-4)
def test_cases(self):
# Test against known results
for unconstrained, error_variance, constrained in self.cases:
result = tools.constrain_stationary_multivariate(
unconstrained, error_variance)
assert_allclose(result[0], constrained)
# Test that the constrained results correspond to companion matrices
# with eigenvalues less than 1 in modulus
for unconstrained in self.eigval_cases:
if type(unconstrained) == list:
cov = np.eye(unconstrained[0].shape[0])
else:
cov = np.eye(unconstrained.shape[0])
constrained, _ = tools.constrain_stationary_multivariate(
unconstrained, cov)
companion = tools.companion_matrix(
[1] + [-constrained[i] for i in range(len(constrained))]).T
assert_equal(
np.max(np.abs(np.linalg.eigvals(companion))) < 1, True)
def test_cases(self):
for constrained in self.constrained_cases:
if type(constrained) == list:
cov = np.eye(constrained[0].shape[0])
else:
cov = np.eye(constrained.shape[0])
unconstrained, _ = tools.unconstrain_stationary_multivariate(
constrained, cov)
reconstrained, _ = tools.constrain_stationary_multivariate(
unconstrained, cov)
assert_allclose(reconstrained, constrained)
for unconstrained in self.unconstrained_cases:
if type(unconstrained) == list:
cov = np.eye(unconstrained[0].shape[0])
else:
cov = np.eye(unconstrained.shape[0])
constrained, _ = tools.constrain_stationary_multivariate(
unconstrained, cov)
reunconstrained, _ = tools.unconstrain_stationary_multivariate(
constrained, cov)
# Note: low tolerance comes from last example in unconstrained_cases,
# but is not a real problem
assert_allclose(reunconstrained, unconstrained, atol=1e-4)
def transform_params(self, unconstrained):
"""
Transform unconstrained parameters used by the optimizer to constrained
parameters used in likelihood evaluation
Parameters
----------
unconstrained : array_like
Array of unconstrained parameters used by the optimizer, to be
transformed.
Returns
-------
constrained : array_like
Array of constrained parameters which may be used in likelihood
evalation.
Notes
-----
Constrains the factor transition to be stationary and variances to be
positive.
"""
unconstrained = np.array(unconstrained, ndmin=1)
constrained = np.zeros(unconstrained.shape, dtype=unconstrained.dtype)
# 1. Intercept terms: nothing to do
constrained[self._params_trend] = unconstrained[self._params_trend]
# 2. AR terms: optionally force to be stationary
if self.k_ar > 0 and self.enforce_stationarity:
# Create the state covariance matrix
if self.error_cov_type == 'diagonal':
state_cov = np.diag(unconstrained[self._params_state_cov]**2)
elif self.error_cov_type == 'unstructured':
state_cov_lower = np.zeros(self.ssm['state_cov'].shape,
dtype=unconstrained.dtype)
state_cov_lower[self._idx_lower_state_cov] = (
unconstrained[self._params_state_cov])
state_cov = np.dot(state_cov_lower, state_cov_lower.T)
# Transform the parameters
coefficients = unconstrained[self._params_ar].reshape(
self.k_endog, self.k_endog * self.k_ar)
coefficient_matrices, variance = (
constrain_stationary_multivariate(coefficients, state_cov))
constrained[self._params_ar] = coefficient_matrices.ravel()
else:
constrained[self._params_ar] = unconstrained[self._params_ar]
# 3. MA terms: optionally force to be invertible
if self.k_ma > 0 and self.enforce_invertibility:
# Transform the parameters, using an identity variance matrix
state_cov = np.eye(self.k_endog, dtype=unconstrained.dtype)
coefficients = unconstrained[self._params_ma].reshape(
self.k_endog, self.k_endog * self.k_ma)
coefficient_matrices, variance = (
constrain_stationary_multivariate(coefficients, state_cov))
constrained[self._params_ma] = coefficient_matrices.ravel()
else:
constrained[self._params_ma] = unconstrained[self._params_ma]
# 4. Regression terms: nothing to do
constrained[self._params_regression] = (
unconstrained[self._params_regression])
# 5. State covariance terms
# If we have variances, force them to be positive
if self.error_cov_type == 'diagonal':
constrained[self._params_state_cov] = (
unconstrained[self._params_state_cov]**2)
# Otherwise, nothing needs to be done
elif self.error_cov_type == 'unstructured':
constrained[self._params_state_cov] = (
unconstrained[self._params_state_cov])
# 5. Measurement error variance terms
if self.measurement_error:
# Force these to be positive
constrained[self._params_obs_cov] = (
unconstrained[self._params_obs_cov]**2)
return constrained
def transform_params(self, unconstrained):
"""
Transform unconstrained parameters used by the optimizer to constrained
parameters used in likelihood evaluation
Parameters
----------
unconstrained : array_like
Array of unconstrained parameters used by the optimizer, to be
transformed.
Returns
-------
constrained : array_like
Array of constrained parameters which may be used in likelihood
evalation.
Notes
-----
Constrains the factor transition to be stationary and variances to be
positive.
"""
unconstrained = np.array(unconstrained, ndmin=1)
constrained = np.zeros(unconstrained.shape, dtype=unconstrained.dtype)
# 1. Intercept terms: nothing to do
constrained[self._params_trend] = unconstrained[self._params_trend]
# 2. AR terms: optionally force to be stationary
if self.k_ar > 0 and self.enforce_stationarity:
# Create the state covariance matrix
if self.error_cov_type == 'diagonal':
state_cov = np.diag(unconstrained[self._params_state_cov]**2)
elif self.error_cov_type == 'unstructured':
state_cov_lower = np.zeros(self.ssm['state_cov'].shape,
dtype=unconstrained.dtype)
state_cov_lower[self._idx_lower_state_cov] = (
unconstrained[self._params_state_cov])
state_cov = np.dot(state_cov_lower, state_cov_lower.T)
# Transform the parameters
coefficients = unconstrained[self._params_ar].reshape(
self.k_endog, self.k_endog * self.k_ar)
coefficient_matrices, variance = (
constrain_stationary_multivariate(coefficients, state_cov))
constrained[self._params_ar] = coefficient_matrices.ravel()
else:
constrained[self._params_ar] = unconstrained[self._params_ar]
# 3. MA terms: optionally force to be invertible
if self.k_ma > 0 and self.enforce_invertibility:
# Transform the parameters, using an identity variance matrix
state_cov = np.eye(self.k_endog, dtype=unconstrained.dtype)
coefficients = unconstrained[self._params_ma].reshape(
self.k_endog, self.k_endog * self.k_ma)
coefficient_matrices, variance = (
constrain_stationary_multivariate(coefficients, state_cov))
constrained[self._params_ma] = coefficient_matrices.ravel()
else:
constrained[self._params_ma] = unconstrained[self._params_ma]
# 4. Regression terms: nothing to do
constrained[self._params_regression] = (
unconstrained[self._params_regression])
# 5. State covariance terms
# If we have variances, force them to be positive
if self.error_cov_type == 'diagonal':
constrained[self._params_state_cov] = (
unconstrained[self._params_state_cov]**2)
# Otherwise, nothing needs to be done
elif self.error_cov_type == 'unstructured':
constrained[self._params_state_cov] = (
unconstrained[self._params_state_cov])
# 5. Measurement error variance terms
if self.measurement_error:
# Force these to be positive
constrained[self._params_obs_cov] = (
unconstrained[self._params_obs_cov]**2)
return constrained
