def test_transform_untransform(self):
true_constrained = self.true_params
# Sometimes the parameters given by Stata are not stationary and / or
# invertible, so we need to skip those transformations for those
# parameter sets
self.model.update(self.true_params)
contracted_polynomial_seasonal_ar = self.model.polynomial_seasonal_ar[self.model.polynomial_seasonal_ar.nonzero()]
self.model.enforce_stationarity = (
(self.model.k_ar == 0 or tools.is_invertible(np.r_[1, -self.model.polynomial_ar[1:]])) and
(len(contracted_polynomial_seasonal_ar) <= 1 or tools.is_invertible(np.r_[1, -contracted_polynomial_seasonal_ar[1:]]))
)
contracted_polynomial_seasonal_ma = self.model.polynomial_seasonal_ma[self.model.polynomial_seasonal_ma.nonzero()]
self.model.enforce_invertibility = (
(self.model.k_ma == 0 or tools.is_invertible(np.r_[1, -self.model.polynomial_ma[1:]])) and
(len(contracted_polynomial_seasonal_ma) <= 1 or tools.is_invertible(np.r_[1, -contracted_polynomial_seasonal_ma[1:]]))
)
unconstrained = self.model.untransform_params(true_constrained)
constrained = self.model.transform_params(unconstrained)
assert_almost_equal(constrained, true_constrained, 4)
self.model.enforce_stationarity = True
self.model.enforce_invertibility = True
def validate_params(self, params):
"""
Validate parameter vector by raising ValueError on invalid values.
Parameters
----------
params : array_like
Array of model parameters.
Notes
-----
Primarily checks that the parameters have the right shape and are not
NaN or infinite. Also checks if parameters are consistent with a
stationary process if `enforce_stationarity=True` and that they are
consistent with an invertible process if `enforce_invertibility=True`.
Finally, checks that the variance term is positive, unless
`concentrate_scale=True`.
Examples
--------
>>> spec = SARIMAXSpecification(ar_order=1)
>>> spec.validate_params([-0.5, 4.]) # returns None
>>> spec.validate_params([-0.5, -2])
ValueError: Non-positive variance term.
>>> spec.validate_params([-1.5, 4.])
ValueError: Non-stationary autoregressive polynomial.
"""
# Note: split_params includes basic validation
params = self.split_params(params)
# Specific checks
if self.enforce_stationarity:
if self.k_ar_params:
ar_poly = np.r_[1, -params['ar_params']]
if not is_invertible(ar_poly):
raise ValueError('Non-stationary autoregressive'
' polynomial.')
if self.k_seasonal_ar_params:
seasonal_ar_poly = np.r_[1, -params['seasonal_ar_params']]
if not is_invertible(seasonal_ar_poly):
raise ValueError('Non-stationary seasonal autoregressive'
' polynomial.')
if self.enforce_invertibility:
if self.k_ma_params:
ma_poly = np.r_[1, params['ma_params']]
if not is_invertible(ma_poly):
raise ValueError('Non-invertible moving average'
' polynomial.')
if self.k_seasonal_ma_params:
seasonal_ma_poly = np.r_[1, params['seasonal_ma_params']]
if not is_invertible(seasonal_ma_poly):
raise ValueError('Non-invertible seasonal moving average'
' polynomial.')
if not self.concentrate_scale:
if params['sigma2'] <= 0:
raise ValueError('Non-positive variance term.')
def is_stationary(self):
"""(bool) Is the reduced autoregressive lag poylnomial stationary."""
validate_basic(self.ar_params,
self.k_ar_params,
title='AR coefficients')
validate_basic(self.seasonal_ar_params,
self.k_seasonal_ar_params,
title='seasonal AR coefficients')
ar_stationary = True
seasonal_ar_stationary = True
if self.k_ar_params > 0:
ar_stationary = is_invertible(self.ar_poly.coef)
if self.k_seasonal_ar_params > 0:
seasonal_ar_stationary = is_invertible(self.seasonal_ar_poly.coef)
return ar_stationary and seasonal_ar_stationary
def is_invertible(self):
"""(bool) Is the reduced moving average lag poylnomial invertible."""
# Short-circuit if there is no MA component
validate_basic(self.ma_params,
self.k_ma_params,
title='MA coefficients')
validate_basic(self.seasonal_ma_params,
self.k_seasonal_ma_params,
title='seasonal MA coefficients')
ma_stationary = True
seasonal_ma_stationary = True
if self.k_ma_params > 0:
ma_stationary = is_invertible(self.ma_poly.coef)
if self.k_seasonal_ma_params > 0:
seasonal_ma_stationary = is_invertible(self.seasonal_ma_poly.coef)
return ma_stationary and seasonal_ma_stationary
def test_cases(self):
for polynomial, invertible in self.cases:
assert_equal(tools.is_invertible(polynomial), invertible)
def test_cases(self):
for polynomial, invertible in self.cases:
assert_equal(tools.is_invertible(polynomial), invertible)
n_iterations = 10000
trace = np.zeros((n_iterations + 1, 3))
trace_accepts = np.zeros(n_iterations)
trace[0] = [0, 0, 1.] # Initial values
# Iterations
for s in range(1, n_iterations + 1):
# 1. Gibbs step: draw the states using the simulation smoother
model.update(trace[s - 1], transformed=True)
sim_smoother.simulate()
states = sim_smoother.simulated_state[:, :-1]
# 2. Gibbs step: draw the autoregressive parameters, and apply
# rejection sampling to ensure an invertible lag polynomial
phi = draw_posterior_phi(model, states, trace[s - 1, 2])
while not is_invertible([1, -phi]):
phi = draw_posterior_phi(model, states, trace[s - 1, 2])
trace[s, 0] = phi
# 3. Gibbs step: draw the variance parameter
sigma2 = draw_posterior_sigma2(model, states, phi)
trace[s, 2] = sigma2
# 4. Metropolis-step for the moving-average parameter
theta = trace[s - 1, 1]
proposal = theta + rw_proposal.rvs()
if proposal > -1 and proposal < 1:
acceptance_probability = np.exp(
model.loglike([phi, proposal, sigma2]) -
model.loglike([phi, theta, sigma2]))