def model_local_linear_trend(endog=None, params=None, direct=False):
if endog is None:
y1 = 10.2394
y2 = 4.2039
y3 = 6.123123
endog = np.r_[y1, y2, y3, [1] * 7]
if params is None:
params = [1.993, 8.253, 2.334]
sigma2_y, sigma2_mu, sigma2_beta = params
if direct:
mod = None
# Construct the basic representation
ssm = KalmanSmoother(k_endog=1, k_states=2, k_posdef=2)
ssm.bind(endog)
init = Initialization(ssm.k_states, initialization_type='diffuse')
ssm.initialize(init)
# ssm.filter_univariate = True # should not be required
# Fill in the system matrices for a local level model
ssm['design', 0, 0] = 1
ssm['obs_cov', 0, 0] = sigma2_y
ssm['transition'] = np.array([[1, 1],
[0, 1]])
ssm['selection'] = np.eye(2)
ssm['state_cov'] = np.diag([sigma2_mu, sigma2_beta])
else:
mod = UnobservedComponents(endog, 'lltrend')
mod.update(params)
ssm = mod.ssm
ssm.initialize(Initialization(ssm.k_states, 'diffuse'))
return mod, ssm
def model_local_level(endog=None, params=None, direct=False):
if endog is None:
y1 = 10.2394
endog = np.r_[y1, [1] * 9]
if params is None:
params = [1.993, 8.253]
sigma2_y, sigma2_mu = params
if direct:
mod = None
# Construct the basic representation
ssm = KalmanSmoother(k_endog=1, k_states=1, k_posdef=1)
ssm.bind(endog)
init = Initialization(ssm.k_states, initialization_type='diffuse')
ssm.initialize(init)
# ssm.filter_univariate = True # should not be required
# Fill in the system matrices for a local level model
ssm['design', :] = 1
ssm['obs_cov', :] = sigma2_y
ssm['transition', :] = 1
ssm['selection', :] = 1
ssm['state_cov', :] = sigma2_mu
else:
mod = UnobservedComponents(endog, 'llevel')
mod.update(params)
ssm = mod.ssm
ssm.initialize(Initialization(ssm.k_states, 'diffuse'))
return mod, ssm
def model_local_level(endog=None, params=None, direct=False):
if endog is None:
y1 = 10.2394
endog = np.r_[y1, [1] * 9]
if params is None:
params = [1.993, 8.253]
sigma2_y, sigma2_mu = params
if direct:
mod = None
# Construct the basic representation
ssm = KalmanSmoother(k_endog=1, k_states=1, k_posdef=1)
ssm.bind(endog)
init = Initialization(ssm.k_states, initialization_type='diffuse')
ssm.initialize(init)
# ssm.filter_univariate = True # should not be required
# Fill in the system matrices for a local level model
ssm['design', :] = 1
ssm['obs_cov', :] = sigma2_y
ssm['transition', :] = 1
ssm['selection', :] = 1
ssm['state_cov', :] = sigma2_mu
else:
mod = UnobservedComponents(endog, 'llevel')
mod.update(params)
ssm = mod.ssm
ssm.initialize(Initialization(ssm.k_states, 'diffuse'))
return mod, ssm
def model_local_linear_trend(endog=None, params=None, direct=False):
if endog is None:
y1 = 10.2394
y2 = 4.2039
y3 = 6.123123
endog = np.r_[y1, y2, y3, [1] * 7]
if params is None:
params = [1.993, 8.253, 2.334]
sigma2_y, sigma2_mu, sigma2_beta = params
if direct:
mod = None
# Construct the basic representation
ssm = KalmanSmoother(k_endog=1, k_states=2, k_posdef=2)
ssm.bind(endog)
init = Initialization(ssm.k_states, initialization_type='diffuse')
ssm.initialize(init)
# ssm.filter_univariate = True # should not be required
# Fill in the system matrices for a local level model
ssm['design', 0, 0] = 1
ssm['obs_cov', 0, 0] = sigma2_y
ssm['transition'] = np.array([[1, 1],
[0, 1]])
ssm['selection'] = np.eye(2)
ssm['state_cov'] = np.diag([sigma2_mu, sigma2_beta])
else:
mod = UnobservedComponents(endog, 'lltrend')
mod.update(params)
ssm = mod.ssm
ssm.initialize(Initialization(ssm.k_states, 'diffuse'))
return mod, ssm
def test_matrices_somewhat_complicated_model():
values = dta.copy()
model = UnobservedComponents(values['unemp'],
level='lltrend',
freq_seasonal=[{'period': 4},
{'period': 9, 'harmonics': 3}],
cycle=True,
cycle_period_bounds=[2, 30],
damped_cycle=True,
stochastic_freq_seasonal=[True, False],
stochastic_cycle=True
)
# Selected parameters
params = [1, # irregular_var
3, 4, # lltrend parameters: level_var, trend_var
5, # freq_seasonal parameters: freq_seasonal_var_0
# cycle parameters: cycle_var, cycle_freq, cycle_damp
6, 2*np.pi/30., .9
]
model.update(params)
# Check scalar properties
assert_equal(model.k_states, 2 + 4 + 6 + 2)
assert_equal(model.k_state_cov, 2 + 1 + 0 + 1)
assert_equal(model.loglikelihood_burn, 2 + 4 + 6 + 2)
assert_allclose(model.ssm.k_posdef, 2 + 4 + 0 + 2)
assert_equal(model.k_params, len(params))
# Check the statespace model matrices against hand-constructed answers
# We group the terms by the component
expected_design = np.r_[[1, 0],
[1, 0, 1, 0],
[1, 0, 1, 0, 1, 0],
[1, 0]].reshape(1, 14)
assert_allclose(model.ssm.design[:, :, 0], expected_design)
expected_transition = __direct_sum([
np.array([[1, 1],
[0, 1]]),
np.array([[0, 1, 0, 0],
[-1, 0, 0, 0],
[0, 0, -1, 0],
[0, 0, 0, -1]]),
np.array([[np.cos(2*np.pi*1/9.), np.sin(2*np.pi*1/9.), 0, 0, 0, 0],
[-np.sin(2*np.pi*1/9.), np.cos(2*np.pi*1/9.), 0, 0, 0, 0],
[0, 0, np.cos(2*np.pi*2/9.), np.sin(2*np.pi*2/9.), 0, 0],
[0, 0, -np.sin(2*np.pi*2/9.), np.cos(2*np.pi*2/9.), 0, 0],
[0, 0, 0, 0, np.cos(2*np.pi/3.), np.sin(2*np.pi/3.)],
[0, 0, 0, 0, -np.sin(2*np.pi/3.), np.cos(2*np.pi/3.)]]),
np.array([[.9*np.cos(2*np.pi/30.), .9*np.sin(2*np.pi/30.)],
[-.9*np.sin(2*np.pi/30.), .9*np.cos(2*np.pi/30.)]])
])
assert_allclose(
model.ssm.transition[:, :, 0], expected_transition, atol=1e-7)
# Since the second seasonal term is not stochastic,
# the dimensionality of the state disturbance is 14 - 6 = 8
expected_selection = np.zeros((14, 14 - 6))
expected_selection[0:2, 0:2] = np.eye(2)
expected_selection[2:6, 2:6] = np.eye(4)
expected_selection[-2:, -2:] = np.eye(2)
assert_allclose(model.ssm.selection[:, :, 0], expected_selection)
expected_state_cov = __direct_sum([
np.diag(params[1:3]),
np.eye(4)*params[3],
np.eye(2)*params[4]
])
assert_allclose(model.ssm.state_cov[:, :, 0], expected_state_cov)
def test_matrices_somewhat_complicated_model():
values = dta.copy()
model = UnobservedComponents(values['unemp'],
level='lltrend',
freq_seasonal=[{'period': 4},
{'period': 9, 'harmonics': 3}],
cycle=True,
cycle_period_bounds=[2, 30],
damped_cycle=True,
stochastic_freq_seasonal=[True, False],
stochastic_cycle=True
)
# Selected parameters
params = [1, # irregular_var
3, 4, # lltrend parameters: level_var, trend_var
5, # freq_seasonal parameters: freq_seasonal_var_0
# cycle parameters: cycle_var, cycle_freq, cycle_damp
6, 2*np.pi/30., .9
]
model.update(params)
# Check scalar properties
assert_equal(model.k_states, 2 + 4 + 6 + 2)
assert_equal(model.k_state_cov, 2 + 1 + 0 + 1)
assert_equal(model.loglikelihood_burn, 2 + 4 + 6 + 2)
assert_allclose(model.ssm.k_posdef, 2 + 4 + 0 + 2)
assert_equal(model.k_params, len(params))
# Check the statespace model matrices against hand-constructed answers
# We group the terms by the component
expected_design = np.r_[[1, 0],
[1, 0, 1, 0],
[1, 0, 1, 0, 1, 0],
[1, 0]].reshape(1, 14)
assert_allclose(model.ssm.design[:, :, 0], expected_design)
expected_transition = __direct_sum([
np.array([[1, 1],
[0, 1]]),
np.array([[0, 1, 0, 0],
[-1, 0, 0, 0],
[0, 0, -1, 0],
[0, 0, 0, -1]]),
np.array([[np.cos(2*np.pi*1/9.), np.sin(2*np.pi*1/9.), 0, 0, 0, 0],
[-np.sin(2*np.pi*1/9.), np.cos(2*np.pi*1/9.), 0, 0, 0, 0],
[0, 0, np.cos(2*np.pi*2/9.), np.sin(2*np.pi*2/9.), 0, 0],
[0, 0, -np.sin(2*np.pi*2/9.), np.cos(2*np.pi*2/9.), 0, 0],
[0, 0, 0, 0, np.cos(2*np.pi/3.), np.sin(2*np.pi/3.)],
[0, 0, 0, 0, -np.sin(2*np.pi/3.), np.cos(2*np.pi/3.)]]),
np.array([[.9*np.cos(2*np.pi/30.), .9*np.sin(2*np.pi/30.)],
[-.9*np.sin(2*np.pi/30.), .9*np.cos(2*np.pi/30.)]])
])
assert_allclose(
model.ssm.transition[:, :, 0], expected_transition, atol=1e-7)
# Since the second seasonal term is not stochastic,
# the dimensionality of the state disturbance is 14 - 6 = 8
expected_selection = np.zeros((14, 14 - 6))
expected_selection[0:2, 0:2] = np.eye(2)
expected_selection[2:6, 2:6] = np.eye(4)
expected_selection[-2:, -2:] = np.eye(2)
assert_allclose(model.ssm.selection[:, :, 0], expected_selection)
expected_state_cov = __direct_sum([
np.diag(params[1:3]),
np.eye(4)*params[3],
np.eye(2)*params[4]
])
assert_allclose(model.ssm.state_cov[:, :, 0], expected_state_cov)
