def test_standardized_forecasts_error():
# Simple test that standardized forecasts errors are calculated correctly.
# Just uses a different calculation method on a univariate series.
# Get the dataset
true = results_kalman_filter.uc_uni
data = pd.DataFrame(true['data'],
index=pd.date_range('1947-01-01',
'1995-07-01',
freq='QS'),
columns=['GDP'])
data['lgdp'] = np.log(data['GDP'])
# Fit an ARIMA(1,1,0) to log GDP
mod = sarimax.SARIMAX(data['lgdp'], order=(1, 1, 0))
res = mod.fit(disp=-1)
standardized_forecasts_error = (
res.filter_results.forecasts_error[0] /
np.sqrt(res.filter_results.forecasts_error_cov[0, 0]))
assert_allclose(
res.filter_results.standardized_forecasts_error[0],
standardized_forecasts_error,
)
def __init__(self, alternate_timing=True, *args, **kwargs):
# Dataset
path = current_path + os.sep + 'results/results_wpi1_ar3_stata.csv'
self.stata = pd.read_csv(path)
self.stata.index = pd.date_range(start='1960-01-01',
periods=124,
freq='QS')
# Matlab comparison
path = current_path + os.sep + 'results/results_wpi1_missing_ar3_matlab_ssm.csv'
matlab_names = [
'a1', 'a2', 'a3', 'detP', 'alphahat1', 'alphahat2', 'alphahat3',
'detV', 'eps', 'epsvar', 'eta', 'etavar'
]
self.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names)
# Regression tests data
path = current_path + os.sep + 'results/results_wpi1_missing_ar3_regression.csv'
self.regression = pd.read_csv(path)
# Create missing observations
self.stata['dwpi'] = self.stata['wpi'].diff()
self.stata.ix[10:21, 'dwpi'] = np.nan
self.model = sarimax.SARIMAX(self.stata.ix[1:, 'dwpi'],
order=(3, 0, 0),
hamilton_representation=True,
*args,
**kwargs)
if alternate_timing:
self.model.timing_init_filtered = True
# Parameters from from Stata's sspace MLE estimation
params = np.r_[.5270715, .0952613, .2580355, .5307459]
self.results = self.model.smooth(params, return_ssm=True)
# Calculate the determinant of the covariance matrices (for easy
# comparison to other languages without having to store 2-dim arrays)
self.results.det_predicted_state_cov = np.zeros((1, self.model.nobs))
self.results.det_smoothed_state_cov = np.zeros((1, self.model.nobs))
for i in range(self.model.nobs):
self.results.det_predicted_state_cov[0, i] = np.linalg.det(
self.results.predicted_state_cov[:, :, i])
self.results.det_smoothed_state_cov[0, i] = np.linalg.det(
self.results.smoothed_state_cov[:, :, i])
# Perform simulation smoothing
n_disturbance_variates = ((self.model.k_endog + self.model.k_posdef) *
self.model.nobs)
self.sim = self.model.simulation_smoother()
self.sim.simulate(
disturbance_variates=np.zeros(n_disturbance_variates),
initial_state_variates=np.zeros(self.model.k_states))
def get_dummy_mod(fit=True, pandas=False):
# This tests time-varying parameters regression when in fact the parameters
# are not time-varying, and in fact the regression fit is perfect
endog = np.arange(100)*1.0
exog = 2*endog
if pandas:
index = pd.date_range('1960-01-01', periods=100, freq='MS')
endog = pd.TimeSeries(endog, index=index)
exog = pd.TimeSeries(exog, index=index)
mod = sarimax.SARIMAX(endog, exog=exog, order=(0,0,0), time_varying_regression=True, mle_regression=False)
if fit:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
res = mod.fit(disp=-1)
else:
res = None
return mod, res
def test_fit_misc():
true = results_sarimax.wpi1_stationary
endog = np.diff(true['data'])[1:]
mod = sarimax.SARIMAX(endog, order=(1,0,1), trend='c')
# Test optim_hessian={'opg','oim','cs'}
with warnings.catch_warnings():
warnings.simplefilter("ignore")
res1 = mod.fit(method='ncg', disp=True, optim_hessian='opg')
res2 = mod.fit(method='ncg', disp=True, optim_hessian='oim')
res3 = mod.fit(method='ncg', disp=True, optim_hessian='cs')
assert_raises(NotImplementedError, mod.fit, method='ncg', disp=False, optim_hessian='a')
# Check that the Hessians broadly result in the same optimum
assert_allclose(res1.llf, res2.llf, rtol=1e-2)
assert_allclose(res1.llf, res3.llf, rtol=1e-2)
# Test return_params=True
mod, _ = get_dummy_mod(fit=False)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
res_params = mod.fit(disp=-1, return_params=True)
assert_almost_equal(res_params, [0,0], 7)
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).squeeze()
desired = lfilter(res.polynomial_reduced_ma, res.polynomial_reduced_ar,
np.r_[0, state_shocks[:-1]])
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: 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]
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)
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)
# 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)