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 model_common_level(endog=None, params=None, restricted=False):
if endog is None:
y11 = 10.2394
y21 = 8.2304
endog = np.column_stack([np.r_[y11, [1] * 9], np.r_[y21, [1] * 9]])
if params is None:
params = [0.1111, 3.2324]
theta, sigma2_mu = params
# sigma2_1 = 1
# sigma_12 = 0
# sigma2_2 = 1
if not restricted:
# Construct the basic representation
ssm = KalmanSmoother(k_endog=2, k_states=2, k_posdef=1)
ssm.bind(endog.T)
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 common trend model
ssm['design'] = np.array([[1, 0],
[theta, 1]])
ssm['obs_cov'] = np.eye(2)
ssm['transition'] = np.eye(2)
ssm['selection', 0, 0] = 1
ssm['state_cov', 0, 0] = sigma2_mu
else:
# Construct the basic representation
ssm = KalmanSmoother(k_endog=2, k_states=1, k_posdef=1)
ssm.bind(endog.T)
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'] = np.array([[1, theta]]).T
ssm['obs_cov'] = np.eye(2)
ssm['transition', :] = 1
ssm['selection', :] = 1
ssm['state_cov', :] = sigma2_mu
return ssm
def model_common_level(endog=None, params=None, restricted=False):
if endog is None:
y11 = 10.2394
y21 = 8.2304
endog = np.column_stack([np.r_[y11, [1] * 9], np.r_[y21, [1] * 9]])
if params is None:
params = [0.1111, 3.2324]
theta, sigma2_mu = params
# sigma2_1 = 1
# sigma_12 = 0
# sigma2_2 = 1
if not restricted:
# Construct the basic representation
ssm = KalmanSmoother(k_endog=2, k_states=2, k_posdef=1)
ssm.bind(endog.T)
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 common trend model
ssm['design'] = np.array([[1, 0],
[theta, 1]])
ssm['obs_cov'] = np.eye(2)
ssm['transition'] = np.eye(2)
ssm['selection', 0, 0] = 1
ssm['state_cov', 0, 0] = sigma2_mu
else:
# Construct the basic representation
ssm = KalmanSmoother(k_endog=2, k_states=1, k_posdef=1)
ssm.bind(endog.T)
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'] = np.array([[1, theta]]).T
ssm['obs_cov'] = np.eye(2)
ssm['transition', :] = 1
ssm['selection', :] = 1
ssm['state_cov', :] = sigma2_mu
return ssm