def test_slice_notation():
endog = np.arange(10)*1.0
mod = KalmanFilter(k_endog=1, k_states=2)
mod.bind(endog)
# Test invalid __setitem__
def set_designs():
mod['designs'] = 1
def set_designs2():
mod['designs',0,0] = 1
def set_designs3():
mod[0] = 1
assert_raises(IndexError, set_designs)
assert_raises(IndexError, set_designs2)
assert_raises(IndexError, set_designs3)
# Test invalid __getitem__
assert_raises(IndexError, lambda: mod['designs'])
assert_raises(IndexError, lambda: mod['designs',0,0,0])
assert_raises(IndexError, lambda: mod[0])
# Test valid __setitem__, __getitem__
assert_equal(mod.design[0,0,0], 0)
mod['design',0,0,0] = 1
assert_equal(mod['design'].sum(), 1)
assert_equal(mod.design[0,0,0], 1)
assert_equal(mod['design',0,0,0], 1)
# Test valid __setitem__, __getitem__ with unspecified time index
mod['design'] = np.zeros(mod['design'].shape)
assert_equal(mod.design[0,0], 0)
mod['design',0,0] = 1
assert_equal(mod.design[0,0], 1)
assert_equal(mod['design',0,0], 1)
class Options(object):
def __init__(self, *args, **kwargs):
# Dummy data
endog = np.arange(10)
k_states = 1
self.model = KalmanFilter(k_endog=1, k_states=k_states, *args, **kwargs)
self.model.bind(endog)
def test_no_endog():
# Test for RuntimeError when no endog is provided by the time filtering
# is initialized.
mod = KalmanFilter(k_endog=1, k_states=1)
# directly call the _initialize_filter function
assert_raises(RuntimeError, mod._initialize_filter)
# indirectly call it through filtering
mod.initialize_approximate_diffuse()
assert_raises(RuntimeError, mod.filter)
def test_filter():
# Tests of invalid calls to the filter function
endog = np.ones((10,1))
mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
mod['design', :] = 1
mod['selection', :] = 1
mod['state_cov', :] = 1
# Test default filter results
res = mod.filter()
assert_equal(isinstance(res, FilterResults), True)
def test_loglike():
# Tests of invalid calls to the loglike function
endog = np.ones((10, 1))
mod = KalmanFilter(endog, k_states=1, initialization="approximate_diffuse")
mod["design", :] = 1
mod["selection", :] = 1
mod["state_cov", :] = 1
# Test that self.memory_no_likelihood = True raises an error
mod.memory_no_likelihood = True
assert_raises(RuntimeError, mod.loglike)
assert_raises(RuntimeError, mod.loglikeobs)
def test_missing():
# Datasets
endog = np.arange(10).reshape(10,1)
endog_pre_na = np.ascontiguousarray(np.c_[
endog.copy() * np.nan, endog.copy() * np.nan, endog, endog])
endog_post_na = np.ascontiguousarray(np.c_[
endog, endog, endog.copy() * np.nan, endog.copy() * np.nan])
endog_inject_na = np.ascontiguousarray(np.c_[
endog, endog.copy() * np.nan, endog, endog.copy() * np.nan])
# Base model
mod = KalmanFilter(np.ascontiguousarray(np.c_[endog, endog]), k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf = mod.loglikeobs()
# Model with prepended nans
mod = KalmanFilter(endog_pre_na, k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf_pre_na = mod.loglikeobs()
assert_allclose(llf_pre_na, llf)
# Model with appended nans
mod = KalmanFilter(endog_post_na, k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf_post_na = mod.loglikeobs()
assert_allclose(llf_post_na, llf)
# Model with injected nans
mod = KalmanFilter(endog_inject_na, k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf_inject_na = mod.loglikeobs()
assert_allclose(llf_inject_na, llf)
def test_filter():
# Tests of invalid calls to the filter function
endog = np.ones((10, 1))
mod = KalmanFilter(endog, k_states=1, initialization="approximate_diffuse")
mod["design", :] = 1
mod["selection", :] = 1
mod["state_cov", :] = 1
# Test default filter results
res = mod.filter()
assert_equal(isinstance(res, FilterResults), True)
# Test specified invalid results class
assert_raises(ValueError, mod.filter, results=object)
# Test specified valid results class
res = mod.filter(results=FilterResults)
assert_equal(isinstance(res, FilterResults), True)
def __init__(self, dtype=float, **kwargs):
self.true = results_kalman_filter.uc_bi
self.true_states = pd.DataFrame(self.true["states"])
# GDP and Unemployment, Quarterly, 1948.1 - 1995.3
data = pd.DataFrame(
self.true["data"], index=pd.date_range("1947-01-01", "1995-07-01", freq="QS"), columns=["GDP", "UNEMP"]
)[4:]
data["GDP"] = np.log(data["GDP"])
data["UNEMP"] = data["UNEMP"] / 100
k_states = 6
self.model = KalmanFilter(k_endog=2, k_states=k_states, **kwargs)
self.model.bind(np.ascontiguousarray(data.values))
# Statespace representation
self.model.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]]
self.model.transition[([0, 0, 1, 1, 2, 3, 4, 5], [0, 4, 1, 2, 1, 2, 4, 5], [0, 0, 0, 0, 0, 0, 0, 0])] = [
1,
1,
0,
0,
1,
1,
1,
1,
]
self.model.selection = np.eye(self.model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec, phi_1, phi_2, alpha_1, alpha_2, alpha_3) = np.array(
self.true["parameters"]
)
self.model.design[([1, 1, 1], [1, 2, 3], [0, 0, 0])] = [alpha_1, alpha_2, alpha_3]
self.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
self.model.obs_cov[1, 1, 0] = sigma_ec ** 2
self.model.state_cov[np.diag_indices(k_states) + (np.zeros(k_states, dtype=int),)] = [
sigma_v ** 2,
sigma_e ** 2,
0,
0,
sigma_w ** 2,
sigma_vl ** 2,
]
# Initialization
initial_state = np.zeros((k_states,))
initial_state_cov = np.eye(k_states) * 100
# Initialization: self.modelification
initial_state_cov = np.dot(
np.dot(self.model.transition[:, :, 0], initial_state_cov), self.model.transition[:, :, 0].T
)
self.model.initialize_known(initial_state, initial_state_cov)
def test_slice_notation():
# Test setting and getting state space representation matrices using the
# slice notation.
endog = np.arange(10) * 1.0
mod = KalmanFilter(k_endog=1, k_states=2)
mod.bind(endog)
# Test invalid __setitem__
def set_designs():
mod["designs"] = 1
def set_designs2():
mod["designs", 0, 0] = 1
def set_designs3():
mod[0] = 1
assert_raises(IndexError, set_designs)
assert_raises(IndexError, set_designs2)
assert_raises(IndexError, set_designs3)
# Test invalid __getitem__
assert_raises(IndexError, lambda: mod["designs"])
assert_raises(IndexError, lambda: mod["designs", 0, 0, 0])
assert_raises(IndexError, lambda: mod[0])
# Test valid __setitem__, __getitem__
assert_equal(mod.design[0, 0, 0], 0)
mod["design", 0, 0, 0] = 1
assert_equal(mod["design"].sum(), 1)
assert_equal(mod.design[0, 0, 0], 1)
assert_equal(mod["design", 0, 0, 0], 1)
# Test valid __setitem__, __getitem__ with unspecified time index
mod["design"] = np.zeros(mod["design"].shape)
assert_equal(mod.design[0, 0], 0)
mod["design", 0, 0] = 1
assert_equal(mod.design[0, 0], 1)
assert_equal(mod["design", 0, 0], 1)
def __init__(self, dtype=float, **kwargs):
self.true = results_kalman_filter.uc_uni
self.true_states = pd.DataFrame(self.true['states'])
# GDP, Quarterly, 1947.1 - 1995.3
data = pd.DataFrame(
self.true['data'],
index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'),
columns=['GDP']
)
data['lgdp'] = np.log(data['GDP'])
# Construct the statespace representation
k_states = 4
self.model = KalmanFilter(k_endog=1, k_states=k_states, **kwargs)
self.model.bind(data['lgdp'].values)
self.model.design[:, :, 0] = [1, 1, 0, 0]
self.model.transition[([0, 0, 1, 1, 2, 3],
[0, 3, 1, 2, 1, 3],
[0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1]
self.model.selection = np.eye(self.model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array(
self.true['parameters']
)
self.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
self.model.state_cov[
np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [
sigma_v**2, sigma_e**2, 0, sigma_w**2
]
# Initialization
initial_state = np.zeros((k_states,))
initial_state_cov = np.eye(k_states)*100
# Initialization: modification
initial_state_cov = np.dot(
np.dot(self.model.transition[:, :, 0], initial_state_cov),
self.model.transition[:, :, 0].T
)
self.model.initialize_known(initial_state, initial_state_cov)
def test_impulse_responses():
# Test for impulse response functions
# Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
# for all periods
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10)
desired = np.ones((11, 1))
assert_allclose(actual, desired)
# Random walk: 2-unit impulse response (i.e. non-orthogonalized irf) is 2
# for all periods
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, impulse=[2])
desired = np.ones((11, 1)) * 2
assert_allclose(actual, desired)
# Random walk: 1-standard-deviation response (i.e. orthogonalized irf) is
# sigma for all periods (here sigma^2 = 2)
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, orthogonalized=True)
desired = np.ones((11, 1)) * 2**0.5
assert_allclose(actual, desired)
# Random walk: 1-standard-deviation cumulative response (i.e. cumulative
# orthogonalized irf)
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10,
orthogonalized=True,
cumulative=True)
desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]
actual = mod.impulse_responses(steps=10,
impulse=[1],
orthogonalized=True,
cumulative=True)
desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]
assert_allclose(actual, desired)
# Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
# for all periods, even when intercepts are present
mod = KalmanFilter(k_endog=1, k_states=1)
mod['state_intercept', 0] = 100.
mod['design', 0, 0] = 1.
mod['obs_intercept', 0] = -1000.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10)
desired = np.ones((11, 1))
assert_allclose(actual, desired)
# Univariate model (random walk): test that an error is thrown when
# a multivariate or empty "impulse" is sent
mod = KalmanFilter(k_endog=1, k_states=1)
assert_raises(ValueError, mod.impulse_responses, impulse=1)
assert_raises(ValueError, mod.impulse_responses, impulse=[1, 1])
assert_raises(ValueError, mod.impulse_responses, impulse=[])
# Univariate model with two uncorrelated shocks
mod = KalmanFilter(k_endog=1, k_states=2)
mod['design', 0, 0:2] = 1.
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.eye(2)
desired = np.ones((11, 1))
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[1, 0])
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[0, 1])
assert_allclose(actual, desired)
# In this case (with sigma=sigma^2=1), orthogonalized is the same as not
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10,
impulse=[1, 0],
orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10,
impulse=[0, 1],
orthogonalized=True)
assert_allclose(actual, desired)
# Univariate model with two correlated shocks
mod = KalmanFilter(k_endog=1, k_states=2)
mod['design', 0, 0:2] = 1.
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])
desired = np.ones((11, 1))
# Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, desired)
# Orthogonalized (i.e. 1-std-dev) impulses now generate different responses
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, desired + desired * 0.5)
actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True)
assert_allclose(actual, desired)
# Multivariate model with two correlated shocks
mod = KalmanFilter(k_endog=2, k_states=2)
mod['design', :, :] = np.eye(2)
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])
ones = np.ones((11, 1))
zeros = np.zeros((11, 1))
# Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's, but
# only for the appropriate series
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, np.c_[ones, zeros])
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, np.c_[zeros, ones])
# Orthogonalized (i.e. 1-std-dev) impulses now generate different
# responses, and only for the appropriate series
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, np.c_[ones, ones * 0.5])
actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True)
assert_allclose(actual, np.c_[zeros, ones])
# AR(1) model generates a geometrically declining series
mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1, 0, 0))
phi = 0.5
mod.update([phi, 1])
desired = np.cumprod(np.r_[1, [phi] * 10])[:, np.newaxis]
# Test going through the model directly
actual = mod.ssm.impulse_responses(steps=10)
assert_allclose(actual, desired)
# Test going through the results object
res = mod.filter([phi, 1.])
actual = res.impulse_responses(steps=10)
assert_allclose(actual, desired)
def test_cython():
# Test the cython _kalman_filter creation, re-creation, calling, etc.
# Check that datatypes are correct:
for prefix, dtype in tools.prefix_dtype_map.items():
endog = np.array(1.0, ndmin=2, dtype=dtype)
mod = KalmanFilter(k_endog=1, k_states=1, dtype=dtype)
# Bind data and initialize the ?KalmanFilter object
mod.bind(endog)
mod._initialize_filter()
# Check that the dtype and prefix are correct
assert_equal(mod.prefix, prefix)
assert_equal(mod.dtype, dtype)
# Test that a dKalmanFilter instance was created
assert_equal(prefix in mod._kalman_filters, True)
kf = mod._kalman_filters[prefix]
assert_equal(isinstance(kf, tools.prefix_kalman_filter_map[prefix]), True)
# Test that the default returned _kalman_filter is the above instance
assert_equal(mod._kalman_filter, kf)
# Check that upcasting datatypes / ?KalmanFilter works (e.g. d -> z)
mod = KalmanFilter(k_endog=1, k_states=1)
# Default dtype is float
assert_equal(mod.prefix, "d")
assert_equal(mod.dtype, np.float64)
# Prior to initialization, no ?KalmanFilter exists
assert_equal(mod._kalman_filter, None)
# Bind data and initialize the ?KalmanFilter object
endog = np.ascontiguousarray(np.array([1.0, 2.0], dtype=np.float64))
mod.bind(endog)
mod._initialize_filter()
kf = mod._kalman_filters["d"]
# Rebind data, still float, check that we haven't changed
mod.bind(endog)
mod._initialize_filter()
assert_equal(mod._kalman_filter, kf)
# Force creating new ?Statespace and ?KalmanFilter, by changing the
# time-varying character of an array
mod.design = np.zeros((1, 1, 2))
mod._initialize_filter()
assert_equal(mod._kalman_filter == kf, False)
kf = mod._kalman_filters["d"]
# Rebind data, now complex, check that the ?KalmanFilter instance has
# changed
endog = np.ascontiguousarray(np.array([1.0, 2.0], dtype=np.complex128))
mod.bind(endog)
assert_equal(mod._kalman_filter == kf, False)
def test_missing():
# Datasets
endog = np.arange(10).reshape(10, 1)
endog_pre_na = np.ascontiguousarray(np.c_[endog.copy() * np.nan,
endog.copy() * np.nan, endog,
endog])
endog_post_na = np.ascontiguousarray(np.c_[endog, endog,
endog.copy() * np.nan,
endog.copy() * np.nan])
endog_inject_na = np.ascontiguousarray(np.c_[endog,
endog.copy() * np.nan, endog,
endog.copy() * np.nan])
# Base model
mod = KalmanFilter(np.ascontiguousarray(np.c_[endog, endog]),
k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog) * 0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf = mod.loglikeobs()
# Model with prepended nans
mod = KalmanFilter(endog_pre_na,
k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog) * 0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf_pre_na = mod.loglikeobs()
assert_allclose(llf_pre_na, llf)
# Model with appended nans
mod = KalmanFilter(endog_post_na,
k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog) * 0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf_post_na = mod.loglikeobs()
assert_allclose(llf_post_na, llf)
# Model with injected nans
mod = KalmanFilter(endog_inject_na,
k_states=1,
initialization='approximate_diffuse')
mod['design', :, :] = 1
mod['obs_cov', :, :] = np.eye(mod.k_endog) * 0.5
mod['transition', :, :] = 0.5
mod['selection', :, :] = 1
mod['state_cov', :, :] = 0.5
llf_inject_na = mod.loglikeobs()
assert_allclose(llf_inject_na, llf)
def test_cython():
# Test the cython _kalman_filter creation, re-creation, calling, etc.
# Check that datatypes are correct:
for prefix, dtype in tools.prefix_dtype_map.items():
endog = np.array(1., ndmin=2, dtype=dtype)
mod = KalmanFilter(k_endog=1, k_states=1, dtype=dtype)
# Bind data and initialize the ?KalmanFilter object
mod.bind(endog)
mod._initialize_filter()
# Check that the dtype and prefix are correct
assert_equal(mod.prefix, prefix)
assert_equal(mod.dtype, dtype)
# Test that a dKalmanFilter instance was created
assert_equal(prefix in mod._kalman_filters, True)
kf = mod._kalman_filters[prefix]
assert_equal(isinstance(kf, tools.prefix_kalman_filter_map[prefix]),
True)
# Test that the default returned _kalman_filter is the above instance
assert_equal(mod._kalman_filter, kf)
# Check that upcasting datatypes / ?KalmanFilter works (e.g. d -> z)
mod = KalmanFilter(k_endog=1, k_states=1)
# Default dtype is float
assert_equal(mod.prefix, 'd')
assert_equal(mod.dtype, np.float64)
# Prior to initialization, no ?KalmanFilter exists
assert_equal(mod._kalman_filter, None)
# Bind data and initialize the ?KalmanFilter object
endog = np.ascontiguousarray(np.array([1., 2.], dtype=np.float64))
mod.bind(endog)
mod._initialize_filter()
kf = mod._kalman_filters['d']
# Rebind data, still float, check that we haven't changed
mod.bind(endog)
mod._initialize_filter()
assert_equal(mod._kalman_filter, kf)
# Force creating new ?Statespace and ?KalmanFilter, by changing the
# time-varying character of an array
mod.design = np.zeros((1, 1, 2))
mod._initialize_filter()
assert_equal(mod._kalman_filter == kf, False)
kf = mod._kalman_filters['d']
# Rebind data, now complex, check that the ?KalmanFilter instance has
# changed
endog = np.ascontiguousarray(np.array([1., 2.], dtype=np.complex128))
mod.bind(endog)
assert_equal(mod._kalman_filter == kf, False)
def test_predict():
# Tests of invalid calls to the predict function
warnings.simplefilter("always")
endog = np.ones((10, 1))
mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
mod['design', :] = 1
mod['obs_intercept'] = np.zeros((1, 10))
mod['selection', :] = 1
mod['state_cov', :] = 1
# Check that we need both forecasts and predicted output for prediction
mod.memory_no_forecast = True
res = mod.filter()
assert_raises(ValueError, res.predict)
mod.memory_no_forecast = False
mod.memory_no_predicted = True
res = mod.filter()
assert_raises(ValueError, res.predict)
mod.memory_no_predicted = False
# Now get a clean filter object
res = mod.filter()
# Check that start < 0 is an error
assert_raises(ValueError, res.predict, start=-1)
# Check that end < start is an error
assert_raises(ValueError, res.predict, start=2, end=1)
# Check that dynamic < 0 is an error
assert_raises(ValueError, res.predict, dynamic=-1)
# Check that dynamic > end is an warning
with warnings.catch_warnings(record=True) as w:
res.predict(end=1, dynamic=2)
message = ('Dynamic prediction specified to begin after the end of'
' prediction, and so has no effect.')
assert_equal(str(w[0].message), message)
# Check that dynamic > nobs is an warning
with warnings.catch_warnings(record=True) as w:
res.predict(end=11, dynamic=11, obs_intercept=np.zeros((1, 1)))
message = ('Dynamic prediction specified to begin during'
' out-of-sample forecasting period, and so has no'
' effect.')
assert_equal(str(w[0].message), message)
# Check for a warning when providing a non-used statespace matrix
with warnings.catch_warnings(record=True) as w:
res.predict(end=res.nobs + 1,
design=True,
obs_intercept=np.zeros((1, 1)))
message = ('Model has time-invariant design matrix, so the design'
' argument to `predict` has been ignored.')
assert_equal(str(w[0].message), message)
# Check that an error is raised when a new time-varying matrix is not
# provided
assert_raises(ValueError, res.predict, end=res.nobs + 1)
# Check that an error is raised when a non-two-dimensional obs_intercept
# is given
assert_raises(ValueError,
res.predict,
end=res.nobs + 1,
obs_intercept=np.zeros(1))
# Check that an error is raised when an obs_intercept with incorrect length
# is given
assert_raises(ValueError,
res.predict,
end=res.nobs + 1,
obs_intercept=np.zeros(2))
# Check that start=None gives start=0 and end=None gives end=nobs
assert_equal(res.predict().forecasts.shape, (1, res.nobs))
# Check that dynamic=True begins dynamic prediction immediately
# TODO just a smoke test
res.predict(dynamic=True)
# Check that on success, PredictionResults object is returned
prediction_results = res.predict(start=3, end=5)
assert_equal(isinstance(prediction_results, PredictionResults), True)
# Check for correctly subset representation arrays
# (k_endog, npredictions) = (1, 2)
assert_equal(prediction_results.endog.shape, (1, 2))
# (k_endog, npredictions) = (1, 2)
assert_equal(prediction_results.obs_intercept.shape, (1, 2))
# (k_endog, k_states) = (1, 1)
assert_equal(prediction_results.design.shape, (1, 1))
# (k_endog, k_endog) = (1, 1)
assert_equal(prediction_results.obs_cov.shape, (1, 1))
# (k_state,) = (1,)
assert_equal(prediction_results.state_intercept.shape, (1, ))
# (k_state, npredictions) = (1, 2)
assert_equal(prediction_results.obs_intercept.shape, (1, 2))
# (k_state, k_state) = (1, 1)
assert_equal(prediction_results.transition.shape, (1, 1))
# (k_state, k_posdef) = (1, 1)
assert_equal(prediction_results.selection.shape, (1, 1))
# (k_posdef, k_posdef) = (1, 1)
assert_equal(prediction_results.state_cov.shape, (1, 1))
# Check for correctly subset filter output arrays
# (k_endog, npredictions) = (1, 2)
assert_equal(prediction_results.forecasts.shape, (1, 2))
assert_equal(prediction_results.forecasts_error.shape, (1, 2))
# (k_states, npredictions) = (1, 2)
assert_equal(prediction_results.filtered_state.shape, (1, 2))
assert_equal(prediction_results.predicted_state.shape, (1, 2))
# (k_endog, k_endog, npredictions) = (1, 1, 2)
assert_equal(prediction_results.forecasts_error_cov.shape, (1, 1, 2))
# (k_states, k_states, npredictions) = (1, 1, 2)
assert_equal(prediction_results.filtered_state_cov.shape, (1, 1, 2))
assert_equal(prediction_results.predicted_state_cov.shape, (1, 1, 2))
# Check for invalid attribute
assert_raises(AttributeError, getattr, prediction_results, 'test')
# Check that an error is raised when a non-two-dimensional obs_cov
# is given
# ...and...
# Check that an error is raised when an obs_cov with incorrect length
# is given
mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
mod['design', :] = 1
mod['obs_cov'] = np.zeros((1, 1, 10))
mod['selection', :] = 1
mod['state_cov', :] = 1
res = mod.filter()
assert_raises(ValueError,
res.predict,
end=res.nobs + 1,
obs_cov=np.zeros((1, 1)))
assert_raises(ValueError,
res.predict,
end=res.nobs + 1,
obs_cov=np.zeros((1, 1, 2)))
class Clark1989(object):
"""
Clark's (1989) bivariate unobserved components model of real GDP (as
presented in Kim and Nelson, 1999)
Tests two-dimensional observation data.
Test data produced using GAUSS code described in Kim and Nelson (1999) and
found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm
See `results.results_kalman_filter` for more information.
"""
def __init__(self, dtype=float, **kwargs):
self.true = results_kalman_filter.uc_bi
self.true_states = pd.DataFrame(self.true['states'])
# GDP and Unemployment, Quarterly, 1948.1 - 1995.3
data = pd.DataFrame(
self.true['data'],
index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'),
columns=['GDP', 'UNEMP']
)[4:]
data['GDP'] = np.log(data['GDP'])
data['UNEMP'] = (data['UNEMP']/100)
k_states = 6
self.model = KalmanFilter(k_endog=2, k_states=k_states, **kwargs)
self.model.bind(np.ascontiguousarray(data.values))
# Statespace representation
self.model.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]]
self.model.transition[
([0, 0, 1, 1, 2, 3, 4, 5],
[0, 4, 1, 2, 1, 2, 4, 5],
[0, 0, 0, 0, 0, 0, 0, 0])
] = [1, 1, 0, 0, 1, 1, 1, 1]
self.model.selection = np.eye(self.model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec,
phi_1, phi_2, alpha_1, alpha_2, alpha_3) = np.array(
self.true['parameters'],
)
self.model.design[([1, 1, 1], [1, 2, 3], [0, 0, 0])] = [
alpha_1, alpha_2, alpha_3
]
self.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
self.model.obs_cov[1, 1, 0] = sigma_ec**2
self.model.state_cov[
np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [
sigma_v**2, sigma_e**2, 0, 0, sigma_w**2, sigma_vl**2
]
# Initialization
initial_state = np.zeros((k_states,))
initial_state_cov = np.eye(k_states)*100
# Initialization: self.modelification
initial_state_cov = np.dot(
np.dot(self.model.transition[:, :, 0], initial_state_cov),
self.model.transition[:, :, 0].T
)
self.model.initialize_known(initial_state, initial_state_cov)
def run_filter(self):
# Filter the data
self.results = self.model.filter()
def test_loglike(self):
assert_almost_equal(
# self.results.llf_obs[self.true['start']:].sum(),
self.results.llf_obs[0:].sum(),
self.true['loglike'], 2
)
def test_filtered_state(self):
assert_almost_equal(
self.results.filtered_state[0][self.true['start']:],
self.true_states.iloc[:, 0], 4
)
assert_almost_equal(
self.results.filtered_state[1][self.true['start']:],
self.true_states.iloc[:, 1], 4
)
assert_almost_equal(
self.results.filtered_state[4][self.true['start']:],
self.true_states.iloc[:, 2], 4
)
assert_almost_equal(
self.results.filtered_state[5][self.true['start']:],
self.true_states.iloc[:, 3], 4
)
def test_impulse_responses():
# Test for impulse response functions
# Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
# for all periods
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10)
desired = np.ones((11, 1))
assert_allclose(actual, desired)
# Random walk: 2-unit impulse response (i.e. non-orthogonalized irf) is 2
# for all periods
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, impulse=[2])
desired = np.ones((11, 1)) * 2
assert_allclose(actual, desired)
# Random walk: 1-standard-deviation response (i.e. orthogonalized irf) is
# sigma for all periods (here sigma^2 = 2)
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, orthogonalized=True)
desired = np.ones((11, 1)) * 2**0.5
assert_allclose(actual, desired)
# Random walk: 1-standard-deviation cumulative response (i.e. cumulative
# orthogonalized irf)
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, orthogonalized=True,
cumulative=True)
desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]
actual = mod.impulse_responses(steps=10, impulse=[1], orthogonalized=True,
cumulative=True)
desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]
assert_allclose(actual, desired)
# Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
# for all periods, even when intercepts are present
mod = KalmanFilter(k_endog=1, k_states=1)
mod['state_intercept', 0] = 100.
mod['design', 0, 0] = 1.
mod['obs_intercept', 0] = -1000.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10)
desired = np.ones((11, 1))
assert_allclose(actual, desired)
# Univariate model (random walk): test that an error is thrown when
# a multivariate or empty "impulse" is sent
mod = KalmanFilter(k_endog=1, k_states=1)
assert_raises(ValueError, mod.impulse_responses, impulse=1)
assert_raises(ValueError, mod.impulse_responses, impulse=[1,1])
assert_raises(ValueError, mod.impulse_responses, impulse=[])
# Univariate model with two uncorrelated shocks
mod = KalmanFilter(k_endog=1, k_states=2)
mod['design', 0, 0:2] = 1.
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.eye(2)
desired = np.ones((11, 1))
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[1,0])
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[0,1])
assert_allclose(actual, desired)
# In this case (with sigma=sigma^2=1), orthogonalized is the same as not
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[1,0], orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[0,1], orthogonalized=True)
assert_allclose(actual, desired)
# Univariate model with two correlated shocks
mod = KalmanFilter(k_endog=1, k_states=2)
mod['design', 0, 0:2] = 1.
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])
desired = np.ones((11, 1))
# Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, desired)
# Orthogonalized (i.e. 1-std-dev) impulses now generate different responses
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, desired + desired * 0.5)
actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True)
assert_allclose(actual, desired)
# Multivariate model with two correlated shocks
mod = KalmanFilter(k_endog=2, k_states=2)
mod['design', :, :] = np.eye(2)
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])
ones = np.ones((11, 1))
zeros = np.zeros((11, 1))
# Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's, but
# only for the appropriate series
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, np.c_[ones, zeros])
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, np.c_[zeros, ones])
# Orthogonalized (i.e. 1-std-dev) impulses now generate different
# responses, and only for the appropriate series
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, np.c_[ones, ones * 0.5])
actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True)
assert_allclose(actual, np.c_[zeros, ones])
# AR(1) model generates a geometrically declining series
mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1,0,0))
phi = 0.5
mod.update([phi, 1])
desired = np.cumprod(np.r_[1, [phi]*10])
# Test going through the model directly
actual = mod.ssm.impulse_responses(steps=10)
assert_allclose(actual[:, 0], desired)
# Test going through the results object
res = mod.filter([phi, 1.])
actual = res.impulse_responses(steps=10)
assert_allclose(actual, desired)
def test_impulse_responses():
# Test for impulse response functions
# Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
# for all periods
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10)
desired = np.ones((11, 1))
assert_allclose(actual, desired)
# Random walk: 2-unit impulse response (i.e. non-orthogonalized irf) is 2
# for all periods
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, impulse=[2])
desired = np.ones((11, 1)) * 2
assert_allclose(actual, desired)
# Random walk: 1-standard-deviation response (i.e. orthogonalized irf) is
# sigma for all periods (here sigma^2 = 2)
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, orthogonalized=True)
desired = np.ones((11, 1)) * 2**0.5
assert_allclose(actual, desired)
# Random walk: 1-standard-deviation cumulative response (i.e. cumulative
# orthogonalized irf)
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10, orthogonalized=True,
cumulative=True)
desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]
actual = mod.impulse_responses(steps=10, impulse=[1], orthogonalized=True,
cumulative=True)
desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]
assert_allclose(actual, desired)
# Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
# for all periods, even when intercepts are present
mod = KalmanFilter(k_endog=1, k_states=1)
mod['state_intercept', 0] = 100.
mod['design', 0, 0] = 1.
mod['obs_intercept', 0] = -1000.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
mod['state_cov', 0, 0] = 2.
actual = mod.impulse_responses(steps=10)
desired = np.ones((11, 1))
assert_allclose(actual, desired)
# Univariate model (random walk): test that an error is thrown when
# a multivariate or empty "impulse" is sent
mod = KalmanFilter(k_endog=1, k_states=1)
assert_raises(ValueError, mod.impulse_responses, impulse=1)
assert_raises(ValueError, mod.impulse_responses, impulse=[1,1])
assert_raises(ValueError, mod.impulse_responses, impulse=[])
# Univariate model with two uncorrelated shocks
mod = KalmanFilter(k_endog=1, k_states=2)
mod['design', 0, 0:2] = 1.
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.eye(2)
desired = np.ones((11, 1))
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[1,0])
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[0,1])
assert_allclose(actual, desired)
# In this case (with sigma=sigma^2=1), orthogonalized is the same as not
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[1,0], orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[0,1], orthogonalized=True)
assert_allclose(actual, desired)
# In this case (with sigma=sigma^2=1), orthogonalized is the same as not
actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[1,0], orthogonalized=True)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=[0,1], orthogonalized=True)
assert_allclose(actual, desired)
<<<<<<< HEAD
=======
>>>>>>> upstream/master
# Univariate model with two correlated shocks
mod = KalmanFilter(k_endog=1, k_states=2)
mod['design', 0, 0:2] = 1.
mod['transition', :, :] = np.eye(2)
mod['selection', :, :] = np.eye(2)
mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])
desired = np.ones((11, 1))
# Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's
actual = mod.impulse_responses(steps=10, impulse=0)
assert_allclose(actual, desired)
actual = mod.impulse_responses(steps=10, impulse=1)
assert_allclose(actual, desired)
# Orthogonalized (i.e. 1-std-dev) impulses now generate different responses
class Clark1989(object):
"""
Clark's (1989) bivariate unobserved components model of real GDP (as
presented in Kim and Nelson, 1999)
Tests two-dimensional observation data.
Test data produced using GAUSS code described in Kim and Nelson (1999) and
found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm
See `results.results_kalman_filter` for more information.
"""
def __init__(self, dtype=float, **kwargs):
self.true = results_kalman_filter.uc_bi
self.true_states = pd.DataFrame(self.true['states'])
# GDP and Unemployment, Quarterly, 1948.1 - 1995.3
data = pd.DataFrame(self.true['data'],
index=pd.date_range('1947-01-01',
'1995-07-01',
freq='QS'),
columns=['GDP', 'UNEMP'])[4:]
data['GDP'] = np.log(data['GDP'])
data['UNEMP'] = (data['UNEMP'] / 100)
k_states = 6
self.model = KalmanFilter(k_endog=2, k_states=k_states, **kwargs)
self.model.bind(np.ascontiguousarray(data.values))
# Statespace representation
self.model.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]]
self.model.transition[([0, 0, 1, 1, 2, 3, 4,
5], [0, 4, 1, 2, 1, 2, 4,
5], [0, 0, 0, 0, 0, 0, 0,
0])] = [1, 1, 0, 0, 1, 1, 1, 1]
self.model.selection = np.eye(self.model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec, phi_1, phi_2, alpha_1,
alpha_2, alpha_3) = np.array(self.true['parameters'], )
self.model.design[([1, 1, 1], [1, 2,
3], [0, 0,
0])] = [alpha_1, alpha_2, alpha_3]
self.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
self.model.obs_cov[1, 1, 0] = sigma_ec**2
self.model.state_cov[np.diag_indices(k_states) +
(np.zeros(k_states, dtype=int), )] = [
sigma_v**2, sigma_e**2, 0, 0, sigma_w**2,
sigma_vl**2
]
# Initialization
initial_state = np.zeros((k_states, ))
initial_state_cov = np.eye(k_states) * 100
# Initialization: self.modelification
initial_state_cov = np.dot(
np.dot(self.model.transition[:, :, 0], initial_state_cov),
self.model.transition[:, :, 0].T)
self.model.initialize_known(initial_state, initial_state_cov)
def run_filter(self):
# Filter the data
self.results = self.model.filter()
def test_loglike(self):
assert_almost_equal(
# self.results.llf_obs[self.true['start']:].sum(),
self.results.llf_obs[0:].sum(),
self.true['loglike'],
2)
def test_filtered_state(self):
assert_almost_equal(
self.results.filtered_state[0][self.true['start']:],
self.true_states.iloc[:, 0], 4)
assert_almost_equal(
self.results.filtered_state[1][self.true['start']:],
self.true_states.iloc[:, 1], 4)
assert_almost_equal(
self.results.filtered_state[4][self.true['start']:],
self.true_states.iloc[:, 2], 4)
assert_almost_equal(
self.results.filtered_state[5][self.true['start']:],
self.true_states.iloc[:, 3], 4)
def test_simulate():
# Test for simulation of new time-series
from scipy.signal import lfilter
# Common parameters
nsimulations = 10
sigma2 = 2
measurement_shocks = np.zeros(nsimulations)
state_shocks = np.random.normal(scale=sigma2**0.5, size=nsimulations)
# Random walk model, so simulated series is just the cumulative sum of
# the shocks
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1]]
assert_allclose(actual, desired)
# Local level model, so simulated series is just the cumulative sum of
# the shocks plus the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1, np.cumsum(state_shocks)[:-1] + 1]
assert_allclose(actual, desired)
# Local level-like model with observation and state intercepts, so
# simulated series is just the cumulative sum of the shocks minus the state
# intercept, plus the observation intercept and the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['obs_intercept', 0, 0] = 5.
mod['design', 0, 0] = 1.
mod['state_intercept', 0, 0] = -2.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1 + 5, np.cumsum(state_shocks - 2)[:-1] + 1 + 5]
assert_allclose(actual, desired)
# Model with time-varying observation intercept
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10) * 1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1] + np.arange(1, 10)]
assert_allclose(actual, desired)
# Model with time-varying observation intercept, check that error is raised
# if more simulations are requested than are nobs.
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10) * 1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
assert_raises(ValueError, mod.simulate, nsimulations + 1,
measurement_shocks, state_shocks)
# ARMA(1,1): phi = [0.1], theta = [0.5], sigma^2 = 2
phi = np.r_[0.1]
theta = np.r_[0.5]
mod = sarimax.SARIMAX([0], order=(1, 0, 1))
mod.update(np.r_[phi, theta, sigma2])
actual = mod.ssm.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = lfilter([1, theta], [1, -phi], np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
# SARIMAX(1,0,1)x(1,0,1,4), this time using the results object call
mod = sarimax.SARIMAX([0.1, 0.5, -0.2],
order=(1, 0, 1),
seasonal_order=(1, 0, 1, 4))
res = mod.filter([0.1, 0.5, 0.2, -0.3, 1])
actual = res.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = lfilter(res.polynomial_reduced_ma, res.polynomial_reduced_ar,
np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
def test_predict():
# Tests of invalid calls to the predict function
warnings.simplefilter("always")
endog = np.ones((10, 1))
mod = KalmanFilter(endog, k_states=1, initialization="approximate_diffuse")
mod["design", :] = 1
mod["obs_intercept"] = np.zeros((1, 10))
mod["selection", :] = 1
mod["state_cov", :] = 1
# Check that we need both forecasts and predicted output for prediction
mod.memory_no_forecast = True
res = mod.filter()
assert_raises(ValueError, res.predict)
mod.memory_no_forecast = False
mod.memory_no_predicted = True
res = mod.filter()
assert_raises(ValueError, res.predict)
mod.memory_no_predicted = False
# Now get a clean filter object
res = mod.filter()
# Check that start < 0 is an error
assert_raises(ValueError, res.predict, start=-1)
# Check that end < start is an error
assert_raises(ValueError, res.predict, start=2, end=1)
# Check that dynamic < 0 is an error
assert_raises(ValueError, res.predict, dynamic=-1)
# Check that dynamic > end is an warning
with warnings.catch_warnings(record=True) as w:
res.predict(end=1, dynamic=2)
message = "Dynamic prediction specified to begin after the end of" " prediction, and so has no effect."
assert_equal(str(w[0].message), message)
# Check that dynamic > nobs is an warning
with warnings.catch_warnings(record=True) as w:
res.predict(end=11, dynamic=11, obs_intercept=np.zeros((1, 1)))
message = (
"Dynamic prediction specified to begin during" " out-of-sample forecasting period, and so has no" " effect."
)
assert_equal(str(w[0].message), message)
# Check for a warning when providing a non-used statespace matrix
with warnings.catch_warnings(record=True) as w:
res.predict(end=res.nobs + 1, design=True, obs_intercept=np.zeros((1, 1)))
message = "Model has time-invariant design matrix, so the design" " argument to `predict` has been ignored."
assert_equal(str(w[0].message), message)
# Check that an error is raised when a new time-varying matrix is not
# provided
assert_raises(ValueError, res.predict, end=res.nobs + 1)
# Check that an error is raised when a non-two-dimensional obs_intercept
# is given
assert_raises(ValueError, res.predict, end=res.nobs + 1, obs_intercept=np.zeros(1))
# Check that an error is raised when an obs_intercept with incorrect length
# is given
assert_raises(ValueError, res.predict, end=res.nobs + 1, obs_intercept=np.zeros(2))
# Check that start=None gives start=0 and end=None gives end=nobs
assert_equal(res.predict().shape, (1, res.nobs))
# Check that dynamic=True begins dynamic prediction immediately
# TODO just a smoke test
res.predict(dynamic=True)
# Check that full_results=True yields a FilterResults object
assert_equal(isinstance(res.predict(full_results=True), FilterResults), True)
# Check that an error is raised when a non-two-dimensional obs_cov
# is given
# ...and...
# Check that an error is raised when an obs_cov with incorrect length
# is given
mod = KalmanFilter(endog, k_states=1, initialization="approximate_diffuse")
mod["design", :] = 1
mod["obs_cov"] = np.zeros((1, 1, 10))
mod["selection", :] = 1
mod["state_cov", :] = 1
res = mod.filter()
assert_raises(ValueError, res.predict, end=res.nobs + 1, obs_cov=np.zeros((1, 1)))
assert_raises(ValueError, res.predict, end=res.nobs + 1, obs_cov=np.zeros((1, 1, 2)))
def test_predict():
# Tests of invalid calls to the predict function
warnings.simplefilter("always")
endog = np.ones((10,1))
mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
mod['design', :] = 1
mod['obs_intercept'] = np.zeros((1,10))
mod['selection', :] = 1
mod['state_cov', :] = 1
# Check that we need both forecasts and predicted output for prediction
mod.memory_no_forecast = True
res = mod.filter()
assert_raises(ValueError, res.predict)
mod.memory_no_forecast = False
mod.memory_no_predicted = True
res = mod.filter()
assert_raises(ValueError, res.predict)
mod.memory_no_predicted = False
# Now get a clean filter object
res = mod.filter()
# Check that start < 0 is an error
assert_raises(ValueError, res.predict, start=-1)
# Check that end < start is an error
assert_raises(ValueError, res.predict, start=2, end=1)
# Check that dynamic < 0 is an error
assert_raises(ValueError, res.predict, dynamic=-1)
# Check that dynamic > end is an warning
with warnings.catch_warnings(record=True) as w:
res.predict(end=1, dynamic=2)
message = ('Dynamic prediction specified to begin after the end of'
' prediction, and so has no effect.')
assert_equal(str(w[0].message), message)
# Check that dynamic > nobs is an warning
with warnings.catch_warnings(record=True) as w:
res.predict(end=11, dynamic=11, obs_intercept=np.zeros((1,1)))
message = ('Dynamic prediction specified to begin during'
' out-of-sample forecasting period, and so has no'
' effect.')
assert_equal(str(w[0].message), message)
# Check for a warning when providing a non-used statespace matrix
with warnings.catch_warnings(record=True) as w:
res.predict(end=res.nobs+1, design=True, obs_intercept=np.zeros((1,1)))
message = ('Model has time-invariant design matrix, so the design'
' argument to `predict` has been ignored.')
assert_equal(str(w[0].message), message)
# Check that an error is raised when a new time-varying matrix is not
# provided
assert_raises(ValueError, res.predict, end=res.nobs+1)
# Check that an error is raised when a non-two-dimensional obs_intercept
# is given
assert_raises(ValueError, res.predict, end=res.nobs+1,
obs_intercept=np.zeros(1))
# Check that an error is raised when an obs_intercept with incorrect length
# is given
assert_raises(ValueError, res.predict, end=res.nobs+1,
obs_intercept=np.zeros(2))
# Check that start=None gives start=0 and end=None gives end=nobs
assert_equal(res.predict().forecasts.shape, (1,res.nobs))
# Check that dynamic=True begins dynamic prediction immediately
# TODO just a smoke test
res.predict(dynamic=True)
# Check that on success, PredictionResults object is returned
prediction_results = res.predict(start=3, end=5)
assert_equal(isinstance(prediction_results, PredictionResults), True)
# Check for correctly subset representation arrays
# (k_endog, npredictions) = (1, 2)
assert_equal(prediction_results.endog.shape, (1, 2))
# (k_endog, npredictions) = (1, 2)
assert_equal(prediction_results.obs_intercept.shape, (1, 2))
# (k_endog, k_states) = (1, 1)
assert_equal(prediction_results.design.shape, (1, 1))
# (k_endog, k_endog) = (1, 1)
assert_equal(prediction_results.obs_cov.shape, (1, 1))
# (k_state,) = (1,)
assert_equal(prediction_results.state_intercept.shape, (1,))
# (k_state, npredictions) = (1, 2)
assert_equal(prediction_results.obs_intercept.shape, (1, 2))
# (k_state, k_state) = (1, 1)
assert_equal(prediction_results.transition.shape, (1, 1))
# (k_state, k_posdef) = (1, 1)
assert_equal(prediction_results.selection.shape, (1, 1))
# (k_posdef, k_posdef) = (1, 1)
assert_equal(prediction_results.state_cov.shape, (1, 1))
# Check for correctly subset filter output arrays
# (k_endog, npredictions) = (1, 2)
assert_equal(prediction_results.forecasts.shape, (1, 2))
assert_equal(prediction_results.forecasts_error.shape, (1, 2))
# (k_states, npredictions) = (1, 2)
assert_equal(prediction_results.filtered_state.shape, (1, 2))
assert_equal(prediction_results.predicted_state.shape, (1, 2))
# (k_endog, k_endog, npredictions) = (1, 1, 2)
assert_equal(prediction_results.forecasts_error_cov.shape, (1, 1, 2))
# (k_states, k_states, npredictions) = (1, 1, 2)
assert_equal(prediction_results.filtered_state_cov.shape, (1, 1, 2))
assert_equal(prediction_results.predicted_state_cov.shape, (1, 1, 2))
# Check for invalid attribute
assert_raises(AttributeError, getattr, prediction_results, 'test')
# Check that an error is raised when a non-two-dimensional obs_cov
# is given
# ...and...
# Check that an error is raised when an obs_cov with incorrect length
# is given
mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
mod['design', :] = 1
mod['obs_cov'] = np.zeros((1,1,10))
mod['selection', :] = 1
mod['state_cov', :] = 1
res = mod.filter()
assert_raises(ValueError, res.predict, end=res.nobs+1,
obs_cov=np.zeros((1,1)))
assert_raises(ValueError, res.predict, end=res.nobs+1,
obs_cov=np.zeros((1,1,2)))
class Clark1987(object):
"""
Clark's (1987) univariate unobserved components model of real GDP (as
presented in Kim and Nelson, 1999)
Test data produced using GAUSS code described in Kim and Nelson (1999) and
found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm
See `results.results_kalman_filter` for more information.
"""
def __init__(self, dtype=float, **kwargs):
self.true = results_kalman_filter.uc_uni
self.true_states = pd.DataFrame(self.true['states'])
# GDP, Quarterly, 1947.1 - 1995.3
data = pd.DataFrame(
self.true['data'],
index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'),
columns=['GDP']
)
data['lgdp'] = np.log(data['GDP'])
# Construct the statespace representation
k_states = 4
self.model = KalmanFilter(k_endog=1, k_states=k_states, **kwargs)
self.model.bind(data['lgdp'].values)
self.model.design[:, :, 0] = [1, 1, 0, 0]
self.model.transition[([0, 0, 1, 1, 2, 3],
[0, 3, 1, 2, 1, 3],
[0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1]
self.model.selection = np.eye(self.model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array(
self.true['parameters']
)
self.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
self.model.state_cov[
np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [
sigma_v**2, sigma_e**2, 0, sigma_w**2
]
# Initialization
initial_state = np.zeros((k_states,))
initial_state_cov = np.eye(k_states)*100
# Initialization: modification
initial_state_cov = np.dot(
np.dot(self.model.transition[:, :, 0], initial_state_cov),
self.model.transition[:, :, 0].T
)
self.model.initialize_known(initial_state, initial_state_cov)
def run_filter(self):
# Filter the data
self.results = self.model.filter()
def test_loglike(self):
assert_almost_equal(
self.results.llf_obs[self.true['start']:].sum(),
self.true['loglike'], 5
)
def test_filtered_state(self):
assert_almost_equal(
self.results.filtered_state[0][self.true['start']:],
self.true_states.iloc[:, 0], 4
)
assert_almost_equal(
self.results.filtered_state[1][self.true['start']:],
self.true_states.iloc[:, 1], 4
)
assert_almost_equal(
self.results.filtered_state[3][self.true['start']:],
self.true_states.iloc[:, 2], 4
)
def test_simulate():
# Test for simulation of new time-series
from scipy.signal import lfilter
# Common parameters
nsimulations = 10
sigma2 = 2
measurement_shocks = np.zeros(nsimulations)
state_shocks = np.random.normal(scale=sigma2**0.5, size=nsimulations)
# Random walk model, so simulated series is just the cumulative sum of
# the shocks
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1]]
assert_allclose(actual, desired)
# Local level model, so simulated series is just the cumulative sum of
# the shocks plus the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1, np.cumsum(state_shocks)[:-1] + 1]
assert_allclose(actual, desired)
# Local level-like model with observation and state intercepts, so
# simulated series is just the cumulative sum of the shocks minus the state
# intercept, plus the observation intercept and the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['obs_intercept', 0, 0] = 5.
mod['design', 0, 0] = 1.
mod['state_intercept', 0, 0] = -2.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1 + 5, np.cumsum(state_shocks - 2)[:-1] + 1 + 5]
assert_allclose(actual, desired)
# Model with time-varying observation intercept
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10)*1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1] + np.arange(1, 10)]
assert_allclose(actual, desired)
# Model with time-varying observation intercept, check that error is raised
# if more simulations are requested than are nobs.
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10)*1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
assert_raises(ValueError, mod.simulate, nsimulations+1, measurement_shocks,
state_shocks)
# ARMA(1,1): phi = [0.1], theta = [0.5], sigma^2 = 2
phi = 0.1
theta = 0.5
mod = sarimax.SARIMAX([0], order=(1, 0, 1))
mod.update(np.r_[phi, theta, sigma2])
actual = mod.ssm.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks,
initial_state=np.zeros(mod.k_states))[0].squeeze()
desired = lfilter([1, theta], [1, -phi], np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
# SARIMAX(1,0,1)x(1,0,1,4), this time using the results object call
mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1, 0, 1),
seasonal_order=(1, 0, 1, 4))
res = mod.filter([0.1, 0.5, 0.2, -0.3, 1])
actual = res.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks, initial_state=np.zeros(mod.k_states))
desired = lfilter(
res.polynomial_reduced_ma, res.polynomial_reduced_ar,
np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
def test_kalman_filter_pickle(data):
# Construct the statespace representation
true = results_kalman_filter.uc_uni
k_states = 4
model = KalmanFilter(k_endog=1, k_states=k_states)
model.bind(data['lgdp'].values)
model.design[:, :, 0] = [1, 1, 0, 0]
model.transition[([0, 0, 1, 1, 2, 3],
[0, 3, 1, 2, 1, 3],
[0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1]
model.selection = np.eye(model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array(
true['parameters']
)
model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
model.state_cov[
np.diag_indices(k_states) + (np.zeros(k_states, dtype=int),)] = [
sigma_v ** 2, sigma_e ** 2, 0, sigma_w ** 2
]
# Initialization
initial_state = np.zeros((k_states,))
initial_state_cov = np.eye(k_states) * 100
# Initialization: modification
initial_state_cov = np.dot(
np.dot(model.transition[:, :, 0], initial_state_cov),
model.transition[:, :, 0].T
)
model.initialize_known(initial_state, initial_state_cov)
pkl_mod = cPickle.loads(cPickle.dumps(model))
results = model.filter()
pkl_results = pkl_mod.filter()
assert_allclose(results.llf_obs[true['start']:].sum(),
pkl_results.llf_obs[true['start']:].sum())
assert_allclose(results.filtered_state[0][true['start']:],
pkl_results.filtered_state[0][true['start']:])
assert_allclose(results.filtered_state[1][true['start']:],
pkl_results.filtered_state[1][true['start']:])
assert_allclose(results.filtered_state[3][true['start']:],
pkl_results.filtered_state[3][true['start']:])
class Clark1987(object):
"""
Clark's (1987) univariate unobserved components model of real GDP (as
presented in Kim and Nelson, 1999)
Test data produced using GAUSS code described in Kim and Nelson (1999) and
found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm
See `results.results_kalman_filter` for more information.
"""
def __init__(self, dtype=float, **kwargs):
self.true = results_kalman_filter.uc_uni
self.true_states = pd.DataFrame(self.true['states'])
# GDP, Quarterly, 1947.1 - 1995.3
data = pd.DataFrame(self.true['data'],
index=pd.date_range('1947-01-01',
'1995-07-01',
freq='QS'),
columns=['GDP'])
data['lgdp'] = np.log(data['GDP'])
# Construct the statespace representation
k_states = 4
self.model = KalmanFilter(k_endog=1, k_states=k_states, **kwargs)
self.model.bind(data['lgdp'].values)
self.model.design[:, :, 0] = [1, 1, 0, 0]
self.model.transition[([0, 0, 1, 1, 2,
3], [0, 3, 1, 2, 1,
3], [0, 0, 0, 0, 0,
0])] = [1, 1, 0, 0, 1, 1]
self.model.selection = np.eye(self.model.k_states)
# Update matrices with given parameters
(sigma_v, sigma_e, sigma_w, phi_1,
phi_2) = np.array(self.true['parameters'])
self.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
self.model.state_cov[np.diag_indices(k_states) +
(np.zeros(k_states, dtype=int), )] = [
sigma_v**2, sigma_e**2, 0, sigma_w**2
]
# Initialization
initial_state = np.zeros((k_states, ))
initial_state_cov = np.eye(k_states) * 100
# Initialization: modification
initial_state_cov = np.dot(
np.dot(self.model.transition[:, :, 0], initial_state_cov),
self.model.transition[:, :, 0].T)
self.model.initialize_known(initial_state, initial_state_cov)
def run_filter(self):
# Filter the data
self.results = self.model.filter()
def test_loglike(self):
assert_almost_equal(self.results.llf_obs[self.true['start']:].sum(),
self.true['loglike'], 5)
def test_filtered_state(self):
assert_almost_equal(
self.results.filtered_state[0][self.true['start']:],
self.true_states.iloc[:, 0], 4)
assert_almost_equal(
self.results.filtered_state[1][self.true['start']:],
self.true_states.iloc[:, 1], 4)
assert_almost_equal(
self.results.filtered_state[3][self.true['start']:],
self.true_states.iloc[:, 2], 4)