def test_invalid():
# Invalid initializations (also tests for some invalid calls to set)
assert_raises(ValueError, Initialization, 5, '')
assert_raises(ValueError, Initialization, 5, 'stationary', constant=[1, 2])
assert_raises(ValueError, Initialization, 5, 'stationary',
stationary_cov=[1, 2])
assert_raises(ValueError, Initialization, 5, 'known')
assert_raises(ValueError, Initialization, 5, 'known', constant=[1])
assert_raises(ValueError, Initialization, 5, 'known', stationary_cov=[0])
# Invalid set() / unset() calls
init = Initialization(5)
assert_raises(ValueError, init.set, -1, 'diffuse')
assert_raises(ValueError, init.unset, -1)
assert_raises(ValueError, init.set, 5, 'diffuse')
assert_raises(ValueError, init.set, 'x', 'diffuse')
assert_raises(ValueError, init.unset, 'x')
assert_raises(ValueError, init.set, (1, 2, 3), 'diffuse')
assert_raises(ValueError, init.unset, (1, 2, 3))
init.set(None, 'diffuse')
assert_raises(ValueError, init.set, 1, 'diffuse')
init.clear()
init.set(1, 'diffuse')
assert_raises(ValueError, init.set, None, 'stationary')
init.clear()
assert_raises(ValueError, init.unset, 1)
# Invalid __call__
init = Initialization(2)
assert_raises(ValueError, init)
init = Initialization(2, 'stationary')
assert_raises(ValueError, init)
def setup_class(cls, **kwargs):
k_states = 2
init = Initialization(k_states)
init.set(0, 'diffuse')
init.set(1, 'stationary')
if kwargs.pop('approx', False):
init_approx = Initialization(k_states)
init_approx.set(0, 'approximate_diffuse')
init_approx.set(1, 'stationary')
kwargs['init_approx'] = init_approx
super(CheckVAR1Mixed, cls).setup_class(init=init, **kwargs)
def setup_class(cls, **kwargs):
k_states = 2
init = Initialization(k_states)
init.set(0, 'diffuse')
init.set(1, 'stationary')
if kwargs.pop('approx', False):
init_approx = Initialization(k_states)
init_approx.set(0, 'approximate_diffuse')
init_approx.set(1, 'stationary')
kwargs['init_approx'] = init_approx
super(CheckVAR1Mixed, cls).setup_class(init=init, **kwargs)
def test_invalid():
# Invalid initializations (also tests for some invalid calls to set)
assert_raises(ValueError, Initialization, 5, '')
assert_raises(ValueError, Initialization, 5, 'stationary', constant=[1, 2])
assert_raises(ValueError,
Initialization,
5,
'stationary',
stationary_cov=[1, 2])
assert_raises(ValueError, Initialization, 5, 'known')
assert_raises(ValueError, Initialization, 5, 'known', constant=[1])
assert_raises(ValueError, Initialization, 5, 'known', stationary_cov=[0])
# Invalid set() / unset() calls
init = Initialization(5)
assert_raises(ValueError, init.set, -1, 'diffuse')
assert_raises(ValueError, init.unset, -1)
assert_raises(ValueError, init.set, 5, 'diffuse')
assert_raises(ValueError, init.set, 'x', 'diffuse')
assert_raises(ValueError, init.unset, 'x')
assert_raises(ValueError, init.set, (1, 2, 3), 'diffuse')
assert_raises(ValueError, init.unset, (1, 2, 3))
init.set(None, 'diffuse')
assert_raises(ValueError, init.set, 1, 'diffuse')
init.clear()
init.set(1, 'diffuse')
assert_raises(ValueError, init.set, None, 'stationary')
init.clear()
assert_raises(ValueError, init.unset, 1)
# Invalid __call__
init = Initialization(2)
assert_raises(ValueError, init)
init = Initialization(2, 'stationary')
assert_raises(ValueError, init)
def test_nested():
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(6, 0, 0))
phi = [0.5, -0.2, 0.1, 0.0, 0.1, 0.0]
sigma2 = 2.
mod.update(np.r_[phi, sigma2])
# Create the initialization object as a series of nested objects
init1_1 = Initialization(3)
init1_1_1 = Initialization(2, 'stationary')
init1_1_2 = Initialization(1, 'approximate_diffuse',
approximate_diffuse_variance=1e9)
init1_1.set((0, 2), init1_1_1)
init1_1.set(2, init1_1_2)
init1_2 = Initialization(3)
init1_2_1 = Initialization(1, 'known', constant=[1], stationary_cov=[[2.]])
init1_2.set(0, init1_2_1)
init1_2_2 = Initialization(1, 'diffuse')
init1_2.set(1, init1_2_2)
init1_2_3 = Initialization(1, 'approximate_diffuse')
init1_2.set(2, init1_2_3)
init = Initialization(6)
init.set((0, 3), init1_1)
init.set((3, 6), init1_2)
# Check the output
desired_cov = np.zeros((6, 6))
T = np.array([[0.5, 1],
[-0.2, 0]])
Q = np.array([[sigma2, 0],
[0, 0]])
desired_cov[:2, :2] = solve_discrete_lyapunov(T, Q)
desired_cov[2, 2] = 1e9
desired_cov[3, 3] = 2.
desired_cov[5, 5] = 1e6
check_initialization(mod, init, [0, 0, 0, 1, 0, 0],
np.diag([0, 0, 0, 0, 1, 0]),
desired_cov)
def test_mixed_stationary():
# More specific tests when one or more blocks are initialized as stationary
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(2, 1, 0))
phi = [0.5, -0.2]
sigma2 = 2.
mod.update(np.r_[phi, sigma2])
init = Initialization(mod.k_states)
init.set(0, 'diffuse')
init.set((1, 3), 'stationary')
desired_cov = np.zeros((3, 3))
T = np.array([[0.5, 1],
[-0.2, 0]])
Q = np.diag([sigma2, 0])
desired_cov[1:, 1:] = solve_discrete_lyapunov(T, Q)
check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov)
init.clear()
init.set(0, 'diffuse')
init.set(1, 'stationary')
init.set(2, 'approximate_diffuse')
T = np.array([[0.5]])
Q = np.diag([sigma2])
desired_cov = np.diag([0, np.squeeze(solve_discrete_lyapunov(T, Q)), 1e6])
check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov)
init.clear()
init.set(0, 'diffuse')
init.set(1, 'stationary')
init.set(2, 'stationary')
desired_cov[2, 2] = 0
check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov)
# Test with a VAR model
endog = np.zeros((10, 2))
mod = varmax.VARMAX(endog, order=(1, 0), )
intercept = [1.5, -0.1]
transition = np.array([[0.5, -0.2],
[0.1, 0.8]])
cov = np.array([[1.2, -0.4],
[-0.4, 0.4]])
tril = np.tril_indices(2)
params = np.r_[intercept, transition.ravel(),
np.linalg.cholesky(cov)[tril]]
mod.update(params)
# > stationary, global
init = Initialization(mod.k_states, 'stationary')
desired_intercept = np.linalg.solve(np.eye(2) - transition, intercept)
desired_cov = solve_discrete_lyapunov(transition, cov)
check_initialization(mod, init, desired_intercept, np.diag([0, 0]),
desired_cov)
# > diffuse, global
init.set(None, 'diffuse')
check_initialization(mod, init, [0, 0], np.eye(2), np.diag([0, 0]))
# > stationary, individually
init.unset(None)
init.set(0, 'stationary')
init.set(1, 'stationary')
a, Pinf, Pstar = init(model=mod)
desired_intercept = [intercept[0] / (1 - transition[0, 0]),
intercept[1] / (1 - transition[1, 1])]
desired_cov = np.diag([cov[0, 0] / (1 - transition[0, 0]**2),
cov[1, 1] / (1 - transition[1, 1]**2)])
check_initialization(mod, init, desired_intercept, np.diag([0, 0]),
desired_cov)
def test_mixed_basic():
# Performs a number of tests for setting different initialization for
# different blocks
# - 2-dimensional -
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(2, 0, 0))
phi = [0.5, -0.2]
sigma2 = 2.
mod.update(np.r_[phi, sigma2])
# known has constant
init = Initialization(mod.k_states)
init.set(0, 'known', constant=[1.2])
# > known has constant
init.set(1, 'known', constant=[-0.2])
check_initialization(mod, init, [1.2, -0.2], np.diag([0, 0]),
np.diag([0, 0]))
# > diffuse
init.unset(1)
init.set(1, 'diffuse')
check_initialization(mod, init, [1.2, 0], np.diag([0, 1]), np.diag([0, 0]))
# > approximate diffuse
init.unset(1)
init.set(1, 'approximate_diffuse')
check_initialization(mod, init, [1.2, 0], np.diag([0, 0]),
np.diag([0, 1e6]))
# > stationary
init.unset(1)
init.set(1, 'stationary')
check_initialization(mod, init, [1.2, 0], np.diag([0, 0]), np.diag([0, 0]))
# known has cov
init = Initialization(mod.k_states)
init.set(0, 'known', stationary_cov=np.diag([1]))
init.set(1, 'diffuse')
check_initialization(mod, init, [0, 0], np.diag([0, 1]), np.diag([1, 0]))
# known has both
init = Initialization(mod.k_states)
init.set(0, 'known', constant=[1.2], stationary_cov=np.diag([1]))
init.set(1, 'diffuse')
check_initialization(mod, init, [1.2, 0], np.diag([0, 1]), np.diag([1, 0]))
# - 3-dimensional -
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(3, 0, 0))
# known has constant
init = Initialization(mod.k_states)
init.set((0, 2), 'known', constant=[1.2, -0.2])
init.set(2, 'diffuse')
check_initialization(mod, init, [1.2, -0.2, 0], np.diag([0, 0, 1]),
np.diag([0, 0, 0]))
# known has cov
init = Initialization(mod.k_states)
init.set((0, 2), 'known', stationary_cov=np.diag([1, 4.2]))
init.set(2, 'diffuse')
check_initialization(mod, init, [0, 0, 0], np.diag([0, 0, 1]),
np.diag([1, 4.2, 0]))
# known has both
init = Initialization(mod.k_states)
init.set((0, 2), 'known', constant=[1.2, -0.2],
stationary_cov=np.diag([1, 4.2]))
init.set(2, 'diffuse')
check_initialization(mod, init, [1.2, -0.2, 0], np.diag([0, 0, 1]),
np.diag([1, 4.2, 0]))
def test_nested():
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(6, 0, 0))
phi = [0.5, -0.2, 0.1, 0.0, 0.1, 0.0]
sigma2 = 2.
mod.update(np.r_[phi, sigma2])
# Create the initialization object as a series of nested objects
init1_1 = Initialization(3)
init1_1_1 = Initialization(2, 'stationary')
init1_1_2 = Initialization(1,
'approximate_diffuse',
approximate_diffuse_variance=1e9)
init1_1.set((0, 2), init1_1_1)
init1_1.set(2, init1_1_2)
init1_2 = Initialization(3)
init1_2_1 = Initialization(1, 'known', constant=[1], stationary_cov=[[2.]])
init1_2.set(0, init1_2_1)
init1_2_2 = Initialization(1, 'diffuse')
init1_2.set(1, init1_2_2)
init1_2_3 = Initialization(1, 'approximate_diffuse')
init1_2.set(2, init1_2_3)
init = Initialization(6)
init.set((0, 3), init1_1)
init.set((3, 6), init1_2)
# Check the output
desired_cov = np.zeros((6, 6))
T = np.array([[0.5, 1], [-0.2, 0]])
Q = np.array([[sigma2, 0], [0, 0]])
desired_cov[:2, :2] = solve_discrete_lyapunov(T, Q)
desired_cov[2, 2] = 1e9
desired_cov[3, 3] = 2.
desired_cov[5, 5] = 1e6
check_initialization(mod, init, [0, 0, 0, 1, 0, 0],
np.diag([0, 0, 0, 0, 1, 0]), desired_cov)
def test_mixed_stationary():
# More specific tests when one or more blocks are initialized as stationary
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(2, 1, 0))
phi = [0.5, -0.2]
sigma2 = 2.
mod.update(np.r_[phi, sigma2])
init = Initialization(mod.k_states)
init.set(0, 'diffuse')
init.set((1, 3), 'stationary')
desired_cov = np.zeros((3, 3))
T = np.array([[0.5, 1], [-0.2, 0]])
Q = np.diag([sigma2, 0])
desired_cov[1:, 1:] = solve_discrete_lyapunov(T, Q)
check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov)
init.clear()
init.set(0, 'diffuse')
init.set(1, 'stationary')
init.set(2, 'approximate_diffuse')
T = np.array([[0.5]])
Q = np.diag([sigma2])
desired_cov = np.diag([0, np.squeeze(solve_discrete_lyapunov(T, Q)), 1e6])
check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov)
init.clear()
init.set(0, 'diffuse')
init.set(1, 'stationary')
init.set(2, 'stationary')
desired_cov[2, 2] = 0
check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov)
# Test with a VAR model
endog = np.zeros((10, 2))
mod = varmax.VARMAX(
endog,
order=(1, 0),
)
intercept = [1.5, -0.1]
transition = np.array([[0.5, -0.2], [0.1, 0.8]])
cov = np.array([[1.2, -0.4], [-0.4, 0.4]])
tril = np.tril_indices(2)
params = np.r_[intercept,
transition.ravel(),
np.linalg.cholesky(cov)[tril]]
mod.update(params)
# > stationary, global
init = Initialization(mod.k_states, 'stationary')
desired_intercept = np.linalg.solve(np.eye(2) - transition, intercept)
desired_cov = solve_discrete_lyapunov(transition, cov)
check_initialization(mod, init, desired_intercept, np.diag([0, 0]),
desired_cov)
# > diffuse, global
init.set(None, 'diffuse')
check_initialization(mod, init, [0, 0], np.eye(2), np.diag([0, 0]))
# > stationary, individually
init.unset(None)
init.set(0, 'stationary')
init.set(1, 'stationary')
a, Pinf, Pstar = init(model=mod)
desired_intercept = [
intercept[0] / (1 - transition[0, 0]),
intercept[1] / (1 - transition[1, 1])
]
desired_cov = np.diag([
cov[0, 0] / (1 - transition[0, 0]**2),
cov[1, 1] / (1 - transition[1, 1]**2)
])
check_initialization(mod, init, desired_intercept, np.diag([0, 0]),
desired_cov)
def test_mixed_basic():
# Performs a number of tests for setting different initialization for
# different blocks
# - 2-dimensional -
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(2, 0, 0))
phi = [0.5, -0.2]
sigma2 = 2.
mod.update(np.r_[phi, sigma2])
# known has constant
init = Initialization(mod.k_states)
init.set(0, 'known', constant=[1.2])
# > known has constant
init.set(1, 'known', constant=[-0.2])
check_initialization(mod, init, [1.2, -0.2], np.diag([0, 0]),
np.diag([0, 0]))
# > diffuse
init.unset(1)
init.set(1, 'diffuse')
check_initialization(mod, init, [1.2, 0], np.diag([0, 1]), np.diag([0, 0]))
# > approximate diffuse
init.unset(1)
init.set(1, 'approximate_diffuse')
check_initialization(mod, init, [1.2, 0], np.diag([0, 0]),
np.diag([0, 1e6]))
# > stationary
init.unset(1)
init.set(1, 'stationary')
check_initialization(mod, init, [1.2, 0], np.diag([0, 0]), np.diag([0, 0]))
# known has cov
init = Initialization(mod.k_states)
init.set(0, 'known', stationary_cov=np.diag([1]))
init.set(1, 'diffuse')
check_initialization(mod, init, [0, 0], np.diag([0, 1]), np.diag([1, 0]))
# known has both
init = Initialization(mod.k_states)
init.set(0, 'known', constant=[1.2], stationary_cov=np.diag([1]))
init.set(1, 'diffuse')
check_initialization(mod, init, [1.2, 0], np.diag([0, 1]), np.diag([1, 0]))
# - 3-dimensional -
endog = np.zeros(10)
mod = sarimax.SARIMAX(endog, order=(3, 0, 0))
# known has constant
init = Initialization(mod.k_states)
init.set((0, 2), 'known', constant=[1.2, -0.2])
init.set(2, 'diffuse')
check_initialization(mod, init, [1.2, -0.2, 0], np.diag([0, 0, 1]),
np.diag([0, 0, 0]))
# known has cov
init = Initialization(mod.k_states)
init.set((0, 2), 'known', stationary_cov=np.diag([1, 4.2]))
init.set(2, 'diffuse')
check_initialization(mod, init, [0, 0, 0], np.diag([0, 0, 1]),
np.diag([1, 4.2, 0]))
# known has both
init = Initialization(mod.k_states)
init.set((0, 2),
'known',
constant=[1.2, -0.2],
stationary_cov=np.diag([1, 4.2]))
init.set(2, 'diffuse')
check_initialization(mod, init, [1.2, -0.2, 0], np.diag([0, 0, 1]),
np.diag([1, 4.2, 0]))