def test_mle_reg():
endog = np.arange(100)*1.0
exog = endog*2
# Make the fit not-quite-perfect
endog[::2] += 0.01
endog[1::2] -= 0.01
with warnings.catch_warnings(record=True) as w:
mod1 = UnobservedComponents(endog, irregular=True, exog=exog, mle_regression=False)
res1 = mod1.fit(disp=-1)
mod2 = UnobservedComponents(endog, irregular=True, exog=exog, mle_regression=True)
res2 = mod2.fit(disp=-1)
assert_allclose(res1.regression_coefficients.filtered[0, -1], 0.5, atol=1e-5)
assert_allclose(res2.params[1], 0.5, atol=1e-5)
def test_mle_reg():
endog = np.arange(100)*1.0
exog = endog*2
# Make the fit not-quite-perfect
endog[::2] += 0.01
endog[1::2] -= 0.01
with warnings.catch_warnings(record=True) as w:
mod1 = UnobservedComponents(endog, irregular=True, exog=exog, mle_regression=False)
res1 = mod1.fit(disp=-1)
mod2 = UnobservedComponents(endog, irregular=True, exog=exog, mle_regression=True)
res2 = mod2.fit(disp=-1)
assert_allclose(res1.regression_coefficients.filtered[0, -1], 0.5, atol=1e-5)
assert_allclose(res2.params[1], 0.5, atol=1e-5)
def test_mle_reg(use_exact_diffuse):
endog = np.arange(100) * 1.0
exog = endog * 2
# Make the fit not-quite-perfect
endog[::2] += 0.01
endog[1::2] -= 0.01
with warnings.catch_warnings(record=True):
mod1 = UnobservedComponents(endog,
irregular=True,
exog=exog,
mle_regression=False,
use_exact_diffuse=use_exact_diffuse)
res1 = mod1.fit(disp=-1)
mod2 = UnobservedComponents(endog,
irregular=True,
exog=exog,
mle_regression=True,
use_exact_diffuse=use_exact_diffuse)
res2 = mod2.fit(disp=-1)
assert_allclose(res1.regression_coefficients.filtered[0, -1],
0.5,
atol=1e-5)
assert_allclose(res2.params[1], 0.5, atol=1e-5)
# When the regression component is part of the state vector with exact
# diffuse initialization, we have two diffuse observations
if use_exact_diffuse:
print(res1.predicted_diffuse_state_cov)
assert_equal(res1.nobs_diffuse, 2)
assert_equal(res2.nobs_diffuse, 0)
else:
assert_equal(res1.loglikelihood_burn, 1)
assert_equal(res2.loglikelihood_burn, 0)
class CausalImpact:
"""
Causal inference through counterfactual predictions using a Bayesian structural time-series model.
"""
def __init__(self, data, inter_date, model_args=None):
"""Main constructor.
:param pandas.DataFrame data: input data. Must contain at least 2 columns, one being named 'y'.
See the README for more details.
:param object inter_date: date of intervention. Must be of same type of the data index elements.
This should usually be int of datetime.date
:param {str: object} model_args: parameters of the model
> max_iter: number of samples in the MCMC sampling
> n_seasons: number of seasons in the seasonal component of the BSTS model
"""
self.data = None # Input data, with a reset index
self.data_index = None # Data initial index
self.data_inter = None # Data intervention date, relative to the reset index
self.model = None # statsmodels BSTS model
self.fit = None # statsmodels BSTS fitted model
self.model_args = None # BSTS model arguments
# Checking input arguments
self._check_input(data, inter_date)
self._check_model_args(model_args)
def run(self):
"""Fit the BSTS model to the data.
"""
self.model = UnobservedComponents(
self.data.loc[:self.data_inter - 1, self._obs_col()].values,
exog=self.data.loc[:self.data_inter - 1, self._reg_cols()].values,
level='local linear trend',
seasonal=self.model_args['n_seasons'],
)
self.fit = self.model.fit(
maxiter=self.model_args['max_iter'],
)
def _check_input(self, data, inter_date):
"""Check input data.
:param pandas.DataFrame data: input data. Must contain at least 2 columns, one being named 'y'.
See the README for more details.
:param object inter_date: date of intervention. Must be of same type of the data index elements.
This should usually be int of datetime.date
"""
self.data_index = data.index
self.data = data.reset_index(drop=True)
try:
self.data_inter = self.data_index.tolist().index(inter_date)
except ValueError:
raise ValueError('Input intervention date could not be found in data index.')
def _check_model_args(self, model_args):
"""Check input arguments, and add missing ones if needed.
:return: the valid dict of arguments
:rtype: {str: object}
"""
if model_args is None:
model_args = {}
for key, val in DEFAULT_ARGS.items():
if key not in model_args:
model_args[key] = val
self.model_args = model_args
def _obs_col(self):
"""Get name of column to be modeled in input data.
:return: column name
:rtype: str
"""
return 'y'
def _reg_cols(self):
"""Get names of columns used in the regression component of the model.
:return: the column names
:rtype: pandas.indexes.base.Index
"""
return self.data.columns.difference([self._obs_col()])
def plot_components(self):
"""Plot the estimated components of the model.
"""
self.fit.plot_components(figsize=(15, 9), legend_loc='lower right')
plt.show()
def plot(self):
"""Produce final impact plots.
"""
min_t = 2 if self.model_args['n_seasons'] is None else self.model_args['n_seasons'] + 1
# Data model before date of intervention - allows to evaluate quality of fit
pred = self.fit.get_prediction()
pre_model = pred.predicted_mean
pre_lower = pred.conf_int()['lower y'].values
pre_upper = pred.conf_int()['upper y'].values
pre_model[:min_t] = np.nan
pre_lower[:min_t] = np.nan
pre_upper[:min_t] = np.nan
# Best prediction of y without any intervention
post_pred = self.fit.get_forecast(
steps=self.data.shape[0] - self.data_inter,
exog=self.data.loc[self.data_inter:, self._reg_cols()]
)
post_model = post_pred.predicted_mean
post_lower = post_pred.conf_int()['lower y'].values
post_upper = post_pred.conf_int()['upper y'].values
plt.figure(figsize=(15, 12))
# Observation and regression components
ax1 = plt.subplot(3, 1, 1)
for col in self._reg_cols():
plt.plot(self.data[col], label=col)
plt.plot(np.concatenate([pre_model, post_model]), 'r--', linewidth=2, label='model')
plt.plot(self.data[self._obs_col()], 'k', linewidth=2, label=self._obs_col())
plt.axvline(self.data_inter, c='k', linestyle='--')
plt.fill_between(
self.data.loc[:self.data_inter - 1].index,
pre_lower,
pre_upper,
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.fill_between(
self.data.loc[self.data_inter:].index,
post_lower,
post_upper,
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.setp(ax1.get_xticklabels(), visible=False)
plt.legend(loc='upper left')
plt.title('Observation vs prediction')
# Pointwise difference
ax2 = plt.subplot(312, sharex=ax1)
plt.plot(self.data[self._obs_col()] - np.concatenate([pre_model, post_model]), 'r--', linewidth=2)
plt.plot(self.data.index, np.zeros(self.data.shape[0]), 'g-', linewidth=2)
plt.axvline(self.data_inter, c='k', linestyle='--')
plt.fill_between(
self.data.loc[:self.data_inter - 1].index,
self.data.loc[:self.data_inter - 1, self._obs_col()] - pre_lower,
self.data.loc[:self.data_inter - 1, self._obs_col()] - pre_upper,
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.fill_between(
self.data.loc[self.data_inter:].index,
self.data.loc[self.data_inter:, self._obs_col()] - post_lower,
self.data.loc[self.data_inter:, self._obs_col()] - post_upper,
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.setp(ax2.get_xticklabels(), visible=False)
plt.title('Difference')
# Cumulative impact
ax3 = plt.subplot(313, sharex=ax1)
plt.plot(
self.data.loc[self.data_inter:].index,
(self.data.loc[self.data_inter:, self._obs_col()] - post_model).cumsum(),
'r--', linewidth=2,
)
plt.plot(self.data.index, np.zeros(self.data.shape[0]), 'g-', linewidth=2)
plt.axvline(self.data_inter, c='k', linestyle='--')
plt.fill_between(
self.data.loc[self.data_inter:].index,
(self.data.loc[self.data_inter:, self._obs_col()] - post_lower).cumsum(),
(self.data.loc[self.data_inter:, self._obs_col()] - post_upper).cumsum(),
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.axis([self.data.index[0], self.data.index[-1], None, None])
ax3.set_xticklabels(self.data_index)
plt.title('Cumulative Impact')
plt.xlabel('$T$')
plt.show()
print('Note: the first {} observations are not shown, due to approximate diffuse initialization'.format(min_t))
def summary_forecast(self)
class CausalImpact:
"""
Causal inference through counterfactual predictions using a Bayesian structural time-series model.
"""
def __init__(self, data, inter_date, model_args=None):
"""Main constructor.
:param pandas.DataFrame data: input data. Must contain at least 2 columns, one being named 'y'.
See the README for more details.
:param object inter_date: date of intervention. Must be of same type of the data index elements.
This should usually be int of datetime.date
:param {str: object} model_args: parameters of the model
> max_iter: number of samples in the MCMC sampling
> n_seasons: number of seasons in the seasonal component of the BSTS model
"""
# Publicly exposed attributes
self.data = None # Input data, with a reset index
self.data_index = None # Data initial index
self.data_inter = None # Data intervention date, relative to the reset index
self.model_args = None # BSTS model arguments
self.result = None #
# Private attributes for modeling purposes only
self._model = None # statsmodels BSTS model
self._fit = None # statsmodels BSTS fitted model
# Checking input arguments
self._check_input(data, inter_date)
self._check_model_args(data, model_args)
def _check_input(self, data, inter_date):
"""Check input data.
:param pandas.DataFrame data: input data. Must contain at least 2 columns, one being named 'y'.
See the README for more details.
:param object inter_date: date of intervention. Must be of same type of the data index elements.
This should usually be int of datetime.date
"""
self.data_index = data.index
self.data = data.reset_index(drop=True)
try:
self.data_inter = self.data_index.tolist().index(inter_date)
except ValueError:
raise ValueError('Input intervention date could not be found in data index.')
self.result = data.reset_index(drop=False)
def _check_model_args(self, data, model_args):
"""Check input arguments, and add missing ones if needed.
:return: the valid dict of arguments
:rtype: {str: object}
"""
if model_args is None:
model_args = {}
for key, val in DEFAULT_ARGS.items():
if key not in model_args:
model_args[key] = val
if self.data_inter < model_args['n_seasons']:
raise ValueError('Training data contains more samples than number of seasons in BSTS model.')
self.model_args = model_args
def run(self, return_df=False):
"""Fit the BSTS model to the data.
"""
self._model = UnobservedComponents(
self.data.loc[:self.data_inter - 1, self._obs_col()].values,
exog=self.data.loc[:self.data_inter - 1, self._reg_cols()].values,
level='local linear trend',
seasonal=self.model_args['n_seasons'],
)
self._fit = self._model.fit(
maxiter=self.model_args['max_iter'],
)
self._get_estimates()
self._get_difference_estimates()
self._get_cumulative_estimates()
if return_df:
return self.result
def _get_estimates(self):
"""Extracting model estimate (before and after intervention) as well as 95% confidence interval.
"""
lpred = self._fit.get_prediction() # Left: model before date of intervention (allows to evaluate fit quality)
rpred = self._fit.get_forecast( # Right: best prediction of y without any intervention
steps=self.data.shape[0] - self.data_inter,
exog=self.data.loc[self.data_inter:, self._reg_cols()]
)
# Model prediction
self.result = self.result.assign(pred=np.concatenate([lpred.predicted_mean, rpred.predicted_mean]))
# 95% confidence interval
lower_conf_ints = []
upper_conf_ints = []
for pred in [lpred, rpred]:
conf_int = pred.conf_int()
if isinstance(conf_int, np.ndarray): # As of 0.9.0, statsmodels returns a np.ndarray here
lower_conf_ints.append(conf_int[:, 0])
upper_conf_ints.append(conf_int[:, 1])
else: # instead of a dataframe with "lower y" and "upper y" columns
lower_conf_ints.append(conf_int.loc[:, 'lower y'].values)
upper_conf_ints.append(conf_int.loc[:, 'upper y'].values)
self.result = self.result.assign(pred_conf_int_lower=np.concatenate(lower_conf_ints))
self.result = self.result.assign(pred_conf_int_upper=np.concatenate(upper_conf_ints))
def _get_difference_estimates(self):
"""Extracting the difference between the model prediction and the actuals, as well as the related 95%
confidence interval.
"""
# Difference between actuals and model
self.result = self.result.assign(pred_diff=self.data[self._obs_col()].values - self.result['pred'])
# Confidence interval of the difference
self.result = self.result.assign(
pred_diff_conf_int_lower=self.data[self._obs_col()] - self.result['pred_conf_int_upper']
)
self.result = self.result.assign(
pred_diff_conf_int_upper=self.data[self._obs_col()] - self.result['pred_conf_int_lower']
)
def _get_cumulative_estimates(self):
"""Extracting estimate of the cumulative impact of the intervention, and its 95% confidence interval.
"""
# Cumulative sum of modeled impact
self.result = self.result.assign(cum_impact=0)
self.result.loc[self.data_inter:, 'cum_impact'] = (
self.data[self._obs_col()] - self.result['pred']
).loc[self.data_inter:].cumsum()
# Confidence interval of the cumulative sum
radius_cumsum = np.sqrt(
((self.result['pred'] - self.result['pred_conf_int_lower']).loc[self.data_inter:] ** 2).cumsum()
)
self.result = self.result.assign(cum_impact_conf_int_lower=0, cum_impact_conf_int_upper=0)
self.result.loc[self.data_inter:, 'cum_impact_conf_int_lower'] = \
self.result['cum_impact'].loc[self.data_inter:] - radius_cumsum
self.result.loc[self.data_inter:, 'cum_impact_conf_int_upper'] = \
self.result['cum_impact'].loc[self.data_inter:] + radius_cumsum
def _obs_col(self):
"""Get name of column to be modeled in input data.
:return: column name
:rtype: str
"""
return 'y'
def _reg_cols(self):
"""Get names of columns used in the regression component of the model.
:return: the column names
:rtype: pandas.indexes.base.Index
"""
return self.data.columns.difference([self._obs_col()])
def plot_components(self):
"""Plot the estimated components of the model.
"""
self._fit.plot_components(figsize=(15, 9), legend_loc='lower right')
plt.show()
def plot(self):
"""Produce final impact plots.
Note: the first few observations are not shown due to approximate diffuse initialization.
"""
min_t = 2 if self.model_args['n_seasons'] is None else self.model_args['n_seasons'] + 1
plt.figure(figsize=(15, 12))
# Observation and regression components
ax1 = plt.subplot(3, 1, 1)
for col in self._reg_cols():
plt.plot(self.data[col], label=col)
plt.plot(self.result['pred'].iloc[min_t:], 'r--', linewidth=2, label='model')
plt.plot(self.data[self._obs_col()], 'k', linewidth=2, label=self._obs_col())
plt.axvline(self.data_inter, c='k', linestyle='--')
plt.fill_between(
self.data.index[min_t:],
self.result['pred_conf_int_lower'].iloc[min_t:],
self.result['pred_conf_int_upper'].iloc[min_t:],
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.setp(ax1.get_xticklabels(), visible=False)
plt.legend(loc='upper left')
plt.title('Observation vs prediction')
# Pointwise difference
ax2 = plt.subplot(312, sharex=ax1)
plt.plot(self.result['pred_diff'].iloc[min_t:], 'r--', linewidth=2)
plt.plot(self.data.index, np.zeros(self.data.shape[0]), 'g-', linewidth=2)
plt.axvline(self.data_inter, c='k', linestyle='--')
plt.fill_between(
self.data.index[min_t:],
self.result['pred_diff_conf_int_lower'].iloc[min_t:],
self.result['pred_diff_conf_int_upper'].iloc[min_t:],
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.setp(ax2.get_xticklabels(), visible=False)
plt.title('Difference')
# Cumulative impact
ax3 = plt.subplot(313, sharex=ax1)
plt.plot(self.data.index, self.result['cum_impact'], 'r--', linewidth=2)
plt.plot(self.data.index, np.zeros(self.data.shape[0]), 'g-', linewidth=2)
plt.axvline(self.data_inter, c='k', linestyle='--')
plt.fill_between(
self.data.index,
self.result['cum_impact_conf_int_lower'],
self.result['cum_impact_conf_int_upper'],
facecolor='gray', interpolate=True, alpha=0.25,
)
plt.axis([self.data.index[0], self.data.index[-1], None, None])
ax3.set_xticklabels(self.data_index, rotation=45)
plt.locator_params(axis='x', nbins=min(12, self.data.shape[0]))
plt.title('Cumulative Impact')
plt.xlabel('$T$')
plt.show()
def run_ucm(name):
true = getattr(results_structural, name)
for model in true['models']:
kwargs = model.copy()
kwargs.update(true['kwargs'])
# Make a copy of the data
values = dta.copy()
freq = kwargs.pop('freq', None)
if freq is not None:
values.index = pd.date_range(start='1959-01-01', periods=len(dta),
freq=freq)
# Test pandas exog
if 'exog' in kwargs:
# Default value here is pd.Series object
exog = np.log(values['realgdp'])
# Also allow a check with a 1-dim numpy array
if kwargs['exog'] == 'numpy':
exog = exog.values.squeeze()
kwargs['exog'] = exog
# Create the model
mod = UnobservedComponents(values['unemp'], **kwargs)
# Smoke test for starting parameters, untransform, transform
# Also test that transform and untransform are inverses
mod.start_params
assert_allclose(mod.start_params, mod.transform_params(mod.untransform_params(mod.start_params)))
# Fit the model at the true parameters
res_true = mod.filter(true['params'])
# Check that the cycle bounds were computed correctly
freqstr = freq[0] if freq is not None else values.index.freqstr[0]
if 'cycle_period_bounds' in kwargs:
cycle_period_bounds = kwargs['cycle_period_bounds']
elif freqstr == 'A':
cycle_period_bounds = (1.5, 12)
elif freqstr == 'Q':
cycle_period_bounds = (1.5*4, 12*4)
elif freqstr == 'M':
cycle_period_bounds = (1.5*12, 12*12)
else:
# If we have no information on data frequency, require the
# cycle frequency to be between 0 and pi
cycle_period_bounds = (2, np.inf)
# Test that the cycle frequency bound is correct
assert_equal(mod.cycle_frequency_bound,
(2*np.pi / cycle_period_bounds[1],
2*np.pi / cycle_period_bounds[0])
)
# Test that the likelihood is correct
rtol = true.get('rtol', 1e-7)
atol = true.get('atol', 0)
assert_allclose(res_true.llf, true['llf'], rtol=rtol, atol=atol)
# Smoke test for plot_components
if have_matplotlib:
fig = res_true.plot_components()
plt.close(fig)
# Now fit the model via MLE
with warnings.catch_warnings(record=True) as w:
res = mod.fit(disp=-1)
# If we found a higher likelihood, no problem; otherwise check
# that we're very close to that found by R
if res.llf <= true['llf']:
assert_allclose(res.llf, true['llf'], rtol=1e-4)
# Smoke test for summary
res.summary()
def run_ucm(name):
true = getattr(results_structural, name)
for model in true['models']:
kwargs = model.copy()
kwargs.update(true['kwargs'])
# Make a copy of the data
values = dta.copy()
freq = kwargs.pop('freq', None)
if freq is not None:
values.index = pd.date_range(start='1959-01-01', periods=len(dta),
freq=freq)
# Test pandas exog
if 'exog' in kwargs:
# Default value here is pd.Series object
exog = np.log(values['realgdp'])
# Also allow a check with a 1-dim numpy array
if kwargs['exog'] == 'numpy':
exog = exog.values.squeeze()
kwargs['exog'] = exog
# Create the model
mod = UnobservedComponents(values['unemp'], **kwargs)
# Smoke test for starting parameters, untransform, transform
# Also test that transform and untransform are inverses
mod.start_params
roundtrip = mod.transform_params(
mod.untransform_params(mod.start_params))
assert_allclose(mod.start_params, roundtrip)
# Fit the model at the true parameters
res_true = mod.filter(true['params'])
# Check that the cycle bounds were computed correctly
freqstr = freq[0] if freq is not None else values.index.freqstr[0]
if 'cycle_period_bounds' in kwargs:
cycle_period_bounds = kwargs['cycle_period_bounds']
elif freqstr == 'A':
cycle_period_bounds = (1.5, 12)
elif freqstr == 'Q':
cycle_period_bounds = (1.5*4, 12*4)
elif freqstr == 'M':
cycle_period_bounds = (1.5*12, 12*12)
else:
# If we have no information on data frequency, require the
# cycle frequency to be between 0 and pi
cycle_period_bounds = (2, np.inf)
# Test that the cycle frequency bound is correct
assert_equal(mod.cycle_frequency_bound,
(2*np.pi / cycle_period_bounds[1],
2*np.pi / cycle_period_bounds[0]))
# Test that the likelihood is correct
rtol = true.get('rtol', 1e-7)
atol = true.get('atol', 0)
assert_allclose(res_true.llf, true['llf'], rtol=rtol, atol=atol)
# Optional smoke test for plot_components
try:
import matplotlib.pyplot as plt
try:
from pandas.plotting import register_matplotlib_converters
register_matplotlib_converters()
except ImportError:
pass
fig = plt.figure()
res_true.plot_components(fig=fig)
except ImportError:
pass
# Now fit the model via MLE
with warnings.catch_warnings(record=True):
res = mod.fit(disp=-1)
# If we found a higher likelihood, no problem; otherwise check
# that we're very close to that found by R
if res.llf <= true['llf']:
assert_allclose(res.llf, true['llf'], rtol=1e-4)
# Smoke test for summary
res.summary()
def test_custom_model_fit(rand_data, pre_int_period, post_int_period,
monkeypatch):
fit_mock = mock.Mock()
monkeypatch.setattr(
'causalimpact.main.CausalImpact._process_posterior_inferences',
mock.Mock())
pre_data = rand_data.loc[pre_int_period[0]:pre_int_period[1], :]
model = UnobservedComponents(endog=pre_data.iloc[:, 0],
level='llevel',
exog=pre_data.iloc[:, 1:])
model.fit = fit_mock
CausalImpact(rand_data, pre_int_period, post_int_period, model=model)
fit_mock.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.01 * 1.2),
(None, None), (None, None)],
disp=False,
nseasons=[],
standardize=True)
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=True)
fit_mock.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.01 * 1.2),
(None, None), (None, None)],
disp=True,
nseasons=[],
standardize=True)
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=True,
prior_level_sd=0.01)
fit_mock.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.01 * 1.2),
(None, None), (None, None)],
disp=True,
prior_level_sd=0.01,
nseasons=[],
standardize=True)
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=True,
prior_level_sd=None)
fit_mock.assert_called_with(bounds=[(None, None), (None, None),
(None, None), (None, None)],
disp=True,
prior_level_sd=None,
nseasons=[],
standardize=True)
model = UnobservedComponents(endog=pre_data.iloc[:, 0],
level='llevel',
exog=pre_data.iloc[:, 1:],
freq_seasonal=[{
'period': 3
}])
model.fit = fit_mock
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=True,
prior_level_sd=0.001)
fit_mock.assert_called_with(bounds=[
(None, None), (0.001 / 1.2, 0.001 * 1.2), (None, None), (None, None),
(None, None)
],
disp=True,
prior_level_sd=0.001,
nseasons=[],
standardize=True)
model = UnobservedComponents(endog=pre_data.iloc[:, 0],
level=True,
exog=pre_data.iloc[:, 1],
trend=True,
seasonal=3,
stochastic_level=True)
model.fit = fit_mock
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=True,
prior_level_sd=0.001)
fit_mock.assert_called_with(bounds=[(0.001 / 1.2, 0.001 * 1.2),
(None, None), (None, None)],
disp=True,
prior_level_sd=0.001,
nseasons=[],
standardize=True)
new_pre_data = rand_data.loc[pre_int_period[0]:pre_int_period[1],
['y', 'x1']]
model = UnobservedComponents(endog=new_pre_data.iloc[:, 0],
level='llevel',
exog=new_pre_data.iloc[:, 1:])
model.fit = fit_mock
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=False)
fit_mock.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.01 * 1.2),
(None, None)],
disp=False,
nseasons=[],
standardize=True)
model = UnobservedComponents(endog=new_pre_data.iloc[:, 0],
level='dtrend',
exog=new_pre_data.iloc[:, 1:])
model.fit = fit_mock
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=False)
fit_mock.assert_called_with(bounds=[(None, None), (None, None)],
disp=False,
nseasons=[],
standardize=True)
model = UnobservedComponents(endog=new_pre_data.iloc[:, 0],
level='lltrend',
exog=new_pre_data.iloc[:, 1:])
model.fit = fit_mock
CausalImpact(rand_data,
pre_int_period,
post_int_period,
model=model,
disp=False)
fit_mock.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.01 * 1.2),
(None, None), (None, None)],
disp=False,
nseasons=[],
standardize=True)
def test_default_model_fit(rand_data, pre_int_period, post_int_period,
monkeypatch):
pre_data = rand_data.loc[pre_int_period[0]:pre_int_period[1], :]
fit_mock = mock.Mock()
model = UnobservedComponents(endog=pre_data.iloc[:, 0],
level='llevel',
exog=pre_data.iloc[:, 1:])
model.fit = fit_mock
construct_mock = mock.Mock(return_value=model)
monkeypatch.setattr('causalimpact.main.CausalImpact._get_default_model',
construct_mock)
monkeypatch.setattr(
'causalimpact.main.CausalImpact._process_posterior_inferences',
mock.Mock())
CausalImpact(rand_data, pre_int_period, post_int_period)
model.fit.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.012),
(None, None), (None, None)],
disp=False,
nseasons=[],
standardize=True)
CausalImpact(rand_data, pre_int_period, post_int_period, disp=True)
model.fit.assert_called_with(bounds=[(None, None), (0.01 / 1.2, 0.012),
(None, None), (None, None)],
disp=True,
nseasons=[],
standardize=True)
CausalImpact(rand_data,
pre_int_period,
post_int_period,
disp=True,
prior_level_sd=0.1)
model.fit.assert_called_with(bounds=[(None, None), (0.1 / 1.2, 0.1 * 1.2),
(None, None), (None, None)],
disp=True,
prior_level_sd=0.1,
nseasons=[],
standardize=True)
CausalImpact(rand_data,
pre_int_period,
post_int_period,
disp=True,
prior_level_sd=None)
model.fit.assert_called_with(bounds=[(None, None), (None, None),
(None, None), (None, None)],
disp=True,
prior_level_sd=None,
nseasons=[],
standardize=True)
model = UnobservedComponents(endog=pre_data.iloc[:, 0],
level='llevel',
exog=pre_data.iloc[:, 1:],
freq_seasonal=[{
'period': 3
}])
model.fit = fit_mock
construct_mock = mock.Mock(return_value=model)
monkeypatch.setattr('causalimpact.main.CausalImpact._get_default_model',
construct_mock)
CausalImpact(rand_data,
pre_int_period,
post_int_period,
disp=True,
prior_level_sd=0.001,
nseasons=[{
'period': 3
}])
model.fit.assert_called_with(bounds=[(None, None),
(0.001 / 1.2, 0.001 * 1.2),
(None, None), (None, None),
(None, None)],
disp=True,
prior_level_sd=0.001,
nseasons=[{
'period': 3
}],
standardize=True)
model = UnobservedComponents(endog=pre_data.iloc[:, 0], level='llevel')
model.fit = fit_mock
construct_mock = mock.Mock(return_value=model)
monkeypatch.setattr('causalimpact.main.CausalImpact._get_default_model',
construct_mock)
new_data = pd.DataFrame(np.random.randn(200, 1), columns=['y'])
CausalImpact(new_data, pre_int_period, post_int_period, disp=False)
model.fit.assert_called_with(bounds=[(None, None),
(0.01 / 1.2, 0.01 * 1.2)],
disp=False,
nseasons=[],
standardize=True)
def run_ucm(name, use_exact_diffuse=False):
true = getattr(results_structural, name)
for model in true['models']:
kwargs = model.copy()
kwargs.update(true['kwargs'])
kwargs['use_exact_diffuse'] = use_exact_diffuse
# Make a copy of the data
values = dta.copy()
freq = kwargs.pop('freq', None)
if freq is not None:
values.index = pd.date_range(start='1959-01-01',
periods=len(dta),
freq=freq)
# Test pandas exog
if 'exog' in kwargs:
# Default value here is pd.Series object
exog = np.log(values['realgdp'])
# Also allow a check with a 1-dim numpy array
if kwargs['exog'] == 'numpy':
exog = exog.values.squeeze()
kwargs['exog'] = exog
# Create the model
mod = UnobservedComponents(values['unemp'], **kwargs)
# Smoke test for starting parameters, untransform, transform
# Also test that transform and untransform are inverses
mod.start_params
roundtrip = mod.transform_params(
mod.untransform_params(mod.start_params))
assert_allclose(mod.start_params, roundtrip)
# Fit the model at the true parameters
res_true = mod.filter(true['params'])
# Check that the cycle bounds were computed correctly
freqstr = freq[0] if freq is not None else values.index.freqstr[0]
if 'cycle_period_bounds' in kwargs:
cycle_period_bounds = kwargs['cycle_period_bounds']
elif freqstr == 'A':
cycle_period_bounds = (1.5, 12)
elif freqstr == 'Q':
cycle_period_bounds = (1.5 * 4, 12 * 4)
elif freqstr == 'M':
cycle_period_bounds = (1.5 * 12, 12 * 12)
else:
# If we have no information on data frequency, require the
# cycle frequency to be between 0 and pi
cycle_period_bounds = (2, np.inf)
# Test that the cycle frequency bound is correct
assert_equal(mod.cycle_frequency_bound,
(2 * np.pi / cycle_period_bounds[1],
2 * np.pi / cycle_period_bounds[0]))
# Test that the likelihood is correct
rtol = true.get('rtol', 1e-7)
atol = true.get('atol', 0)
if use_exact_diffuse:
# If we are using exact diffuse initialization, then we need to
# adjust for the fact that KFAS does not include the constant in
# the likelihood function for the diffuse periods
# (see note to test_exact_diffuse_filtering.py for details).
res_llf = (res_true.llf_obs.sum() +
res_true.nobs_diffuse * 0.5 * np.log(2 * np.pi))
else:
# If we are using approximate diffuse initialization, then we need
# to ignore the first period, and this will agree with KFAS (since
# it does not include the constant in the likelihood function for
# diffuse periods).
res_llf = res_true.llf_obs[res_true.loglikelihood_burn:].sum()
assert_allclose(res_llf, true['llf'], rtol=rtol, atol=atol)
# Optional smoke test for plot_components
try:
import matplotlib.pyplot as plt
try:
from pandas.plotting import register_matplotlib_converters
register_matplotlib_converters()
except ImportError:
pass
fig = plt.figure()
res_true.plot_components(fig=fig)
except ImportError:
pass
# Now fit the model via MLE
with warnings.catch_warnings(record=True):
fit_kwargs = {}
if 'maxiter' in true:
fit_kwargs['maxiter'] = true['maxiter']
res = mod.fit(start_params=true.get('start_params', None),
disp=-1,
**fit_kwargs)
# If we found a higher likelihood, no problem; otherwise check
# that we're very close to that found by R
# See note above about these computation
if use_exact_diffuse:
res_llf = (res.llf_obs.sum() +
res.nobs_diffuse * 0.5 * np.log(2 * np.pi))
else:
res_llf = res.llf_obs[res_true.loglikelihood_burn:].sum()
if res_llf <= true['llf']:
assert_allclose(res_llf, true['llf'], rtol=1e-4)
# Smoke test for summary
res.summary()
def test_compile_posterior_inferences_w_data(data):
pre_period = [0, 70]
post_period = [71, 100]
df_pre = data.loc[pre_period[0]:pre_period[1], :]
df_post = data.loc[post_period[0]:post_period[1], :]
post_period_response = None
alpha = 0.05
orig_std_params = (0., 1.)
model = UnobservedComponents(endog=df_pre.iloc[:, 0].values,
level='llevel',
exog=df_pre.iloc[:, 1:].values)
trained_model = model.fit()
inferences = compile_posterior(trained_model, data, df_pre, df_post,
post_period_response, alpha,
orig_std_params)
expected_response = pd.Series(data.iloc[:, 0], name='response')
assert_series_equal(expected_response, inferences['series']['response'])
expected_cumsum = pd.Series(np.cumsum(expected_response),
name='cum_response')
assert_series_equal(expected_cumsum, inferences['series']['cum_response'])
predictor = trained_model.get_prediction()
forecaster = trained_model.get_forecast(
steps=len(df_post),
exog=df_post.iloc[:, 1].values.reshape(-1, 1),
alpha=alpha)
pre_pred = predictor.predicted_mean
post_pred = forecaster.predicted_mean
point_pred = np.concatenate([pre_pred, post_pred])
expected_point_pred = pd.Series(point_pred, name='point_pred')
assert_series_equal(expected_point_pred,
inferences['series']['point_pred'])
pre_ci = pd.DataFrame(predictor.conf_int(alpha=alpha))
pre_ci.index = df_pre.index
post_ci = pd.DataFrame(forecaster.conf_int(alpha=alpha))
post_ci.index = df_post.index
ci = pd.concat([pre_ci, post_ci])
expected_pred_upper = ci.iloc[:, 1]
expected_pred_upper = expected_pred_upper.rename('point_pred_upper')
expected_pred_lower = ci.iloc[:, 0]
expected_pred_lower = expected_pred_lower.rename('point_pred_lower')
assert_series_equal(expected_pred_upper,
inferences['series']['point_pred_upper'])
assert_series_equal(expected_pred_lower,
inferences['series']['point_pred_lower'])
expected_cum_pred = pd.Series(np.cumsum(point_pred), name='cum_pred')
assert_series_equal(expected_cum_pred, inferences['series']['cum_pred'])
expected_cum_pred_lower = pd.Series(np.cumsum(expected_pred_lower),
name='cum_pred_lower')
assert_series_equal(expected_cum_pred_lower,
inferences['series']['cum_pred_lower'])
expected_cum_pred_upper = pd.Series(np.cumsum(expected_pred_upper),
name='cum_pred_upper')
assert_series_equal(expected_cum_pred_upper,
inferences['series']['cum_pred_upper'])
expected_point_effect = pd.Series(expected_response - expected_point_pred,
name='point_effect')
assert_series_equal(expected_point_effect,
inferences['series']['point_effect'])
expected_point_effect_lower = pd.Series(expected_response -
expected_pred_lower,
name='point_effect_lower')
assert_series_equal(expected_point_effect_lower,
inferences['series']['point_effect_lower'])
expected_point_effect_upper = pd.Series(expected_response -
expected_pred_upper,
name='point_effect_upper')
assert_series_equal(expected_point_effect_upper,
inferences['series']['point_effect_upper'])
expected_cum_effect = pd.Series(np.concatenate(
(np.zeros(len(df_pre)),
np.cumsum(expected_point_effect.iloc[len(df_pre):]))),
name='cum_effect')
assert_series_equal(expected_cum_effect,
inferences['series']['cum_effect'])
expected_cum_effect_lower = pd.Series(np.concatenate(
(np.zeros(len(df_pre)),
np.cumsum(expected_point_effect_lower.iloc[len(df_pre):]))),
name='cum_effect_lower')
assert_series_equal(expected_cum_effect_lower,
inferences['series']['cum_effect_lower'])
expected_cum_effect_upper = pd.Series(np.concatenate(
(np.zeros(len(df_pre)),
np.cumsum(expected_point_effect_upper.iloc[len(df_pre):]))),
name='cum_effect_upper')
assert_series_equal(expected_cum_effect_upper,
inferences['series']['cum_effect_upper'])
class CausalImpact:
"""
Causal inference through counterfactual predictions using a Bayesian structural time-series model.
"""
def __init__(self, data, inter_date, n_seasons=7):
"""Main constructor.
:param pandas.DataFrame data: input data. Must contain at least 2 columns, one being named 'y'.
See the README for more details.
:param object inter_date: date of intervention. Must be of same type of the data index elements.
This should usually be int of datetime.date
:param int n_seasons: number of seasons in the seasonal component of the BSTS model
"""
# Constructor arguments
self.data = data.reset_index(
drop=True) # Input data, with a reset index
self.inter_date = inter_date # Date of intervention as passed in input
self.n_seasons = n_seasons # Number of seasons in the seasonal component of the BSTS model
# DataFrame holding the results of the BSTS model predictions.
self.result = None
# Private attributes for modeling purposes only
self._input_index = data.index # Input data index
self._inter_index = None # Data intervention date, relative to the reset index
self._model = None # statsmodels BSTS model
self._fit = None # statsmodels BSTS fitted model
# Checking input arguments
self._check_input()
self._check_model_args()
def _check_input(self):
"""Check input data.
"""
try:
self._inter_index = self._input_index.tolist().index(
self.inter_date)
except ValueError:
raise ValueError(
'Input intervention date could not be found in data index.')
self.result = self.data.copy()
def _check_model_args(self):
"""Check if input arguments are compatible with the data.
"""
if self.n_seasons < 2:
raise ValueError(
'Seasonal component must have a seasonal period of at least 2.'
)
if self._inter_index < self.n_seasons:
raise ValueError(
'Training data contains more samples than number of seasons in BSTS model.'
)
def run(self, max_iter=1000, return_df=False):
"""Fit the BSTS model to the data.
:param int max_iter: max number of iterations in UnobservedComponents.fit (maximum likelihood estimator)
:param bool return_df: set to `True` if you want this method to return the dataframe of model results
:return: None or pandas.DataFrame of results
"""
self._model = UnobservedComponents(
self.data.loc[:self._inter_index - 1,
self._obs_col()].values,
exog=self.data.loc[:self._inter_index - 1,
self._reg_cols()].values,
level='local linear trend',
seasonal=self.n_seasons,
)
self._fit = self._model.fit(maxiter=max_iter)
self._get_estimates()
self._get_difference_estimates()
self._get_cumulative_estimates()
if return_df:
return self.result
def _get_estimates(self):
"""Extracting model estimate (before and after intervention) as well as 95% confidence interval.
"""
lpred = self._fit.get_prediction(
) # Left: model before date of intervention (allows to evaluate fit quality)
rpred = self._fit.get_forecast( # Right: best prediction of y without any intervention
steps=self.data.shape[0] - self._inter_index,
exog=self.data.loc[self._inter_index:,
self._reg_cols()])
# Model prediction
self.result = self.result.assign(
pred=np.concatenate([lpred.predicted_mean, rpred.predicted_mean]))
# 95% confidence interval
lower_conf_ints = []
upper_conf_ints = []
for pred in [lpred, rpred]:
conf_int = pred.conf_int()
if isinstance(
conf_int, np.ndarray
): # As of 0.9.0, statsmodels returns a np.ndarray here
lower_conf_ints.append(conf_int[:, 0])
upper_conf_ints.append(conf_int[:, 1])
else: # instead of a dataframe with "lower y" and "upper y" columns
lower_conf_ints.append(conf_int.loc[:, 'lower y'].values)
upper_conf_ints.append(conf_int.loc[:, 'upper y'].values)
self.result = self.result.assign(
pred_conf_int_lower=np.concatenate(lower_conf_ints))
self.result = self.result.assign(
pred_conf_int_upper=np.concatenate(upper_conf_ints))
def _get_difference_estimates(self):
"""Extracting the difference between the model prediction and the actuals, as well as the related 95%
confidence interval.
"""
# Difference between actuals and model
self.result = self.result.assign(
pred_diff=self.data[self._obs_col()].values - self.result['pred'])
# Confidence interval of the difference
self.result = self.result.assign(
pred_diff_conf_int_lower=self.data[self._obs_col()] -
self.result['pred_conf_int_upper'])
self.result = self.result.assign(
pred_diff_conf_int_upper=self.data[self._obs_col()] -
self.result['pred_conf_int_lower'])
def _get_cumulative_estimates(self):
"""Extracting estimate of the cumulative impact of the intervention, and its 95% confidence interval.
"""
# Cumulative sum of modeled impact
self.result = self.result.assign(cum_impact=0)
self.result.loc[self._inter_index:, 'cum_impact'] = (
self.data[self._obs_col()] -
self.result['pred']).loc[self._inter_index:].cumsum()
# Confidence interval of the cumulative sum
radius_cumsum = np.sqrt(
((self.result['pred'] - self.result['pred_conf_int_lower']
).loc[self._inter_index:]**2).cumsum())
self.result = self.result.assign(cum_impact_conf_int_lower=0,
cum_impact_conf_int_upper=0)
self.result.loc[self._inter_index:, 'cum_impact_conf_int_lower'] = \
self.result['cum_impact'].loc[self._inter_index:] - radius_cumsum
self.result.loc[self._inter_index:, 'cum_impact_conf_int_upper'] = \
self.result['cum_impact'].loc[self._inter_index:] + radius_cumsum
def _obs_col(self):
"""Get name of column to be modeled in input data.
:return: column name
:rtype: str
"""
return 'y'
def _reg_cols(self):
"""Get names of columns used in the regression component of the model.
:return: the column names
:rtype: pandas.indexes.base.Index
"""
return self.data.columns.difference([self._obs_col()])
def plot_components(self):
"""Plot the estimated components of the model.
"""
self._fit.plot_components(figsize=(15, 9), legend_loc='lower right')
plt.show()
def plot(self, split=False):
"""Produce final impact plots.
Note: the first few observations are not shown due to approximate diffuse initialization.
:param bool split: set to `True` if you want to split plot of input data into multiple charts. Default: `False`.
"""
min_t = 2 if self.n_seasons is None else self.n_seasons + 1
n_plots = 3 + split * len(self._reg_cols())
grid = gs.GridSpec(n_plots, 1)
plt.figure(figsize=(15, 4 * n_plots))
# Observation and regression components
ax1 = plt.subplot(grid[0, :])
# Regression components
for i, col in enumerate(self._reg_cols()):
plt.plot(self.data[col], label=col)
if split: # Creating new subplot if charts should be split
plt.axvline(self._inter_index, c='k', linestyle='--')
plt.title(col)
ax = plt.subplot(grid[i + 1, :], sharex=ax1)
plt.setp(ax.get_xticklabels(), visible=False)
# Model and confidence intervals
plt.plot(self.result['pred'].iloc[min_t:],
'r--',
linewidth=2,
label='model')
plt.plot(self.data[self._obs_col()],
'k',
linewidth=2,
label=self._obs_col())
plt.axvline(self._inter_index, c='k', linestyle='--')
plt.fill_between(
self.data.index[min_t:],
self.result['pred_conf_int_lower'].iloc[min_t:],
self.result['pred_conf_int_upper'].iloc[min_t:],
facecolor='gray',
interpolate=True,
alpha=0.25,
)
plt.setp(ax1.get_xticklabels(), visible=False)
plt.legend(loc='upper left')
plt.title('Observation vs prediction')
# Pointwise difference
ax2 = plt.subplot(grid[-2, :], sharex=ax1)
plt.plot(self.result['pred_diff'].iloc[min_t:], 'r--', linewidth=2)
plt.plot(self.data.index,
np.zeros(self.data.shape[0]),
'g-',
linewidth=2)
plt.axvline(self._inter_index, c='k', linestyle='--')
plt.fill_between(
self.data.index[min_t:],
self.result['pred_diff_conf_int_lower'].iloc[min_t:],
self.result['pred_diff_conf_int_upper'].iloc[min_t:],
facecolor='gray',
interpolate=True,
alpha=0.25,
)
plt.setp(ax2.get_xticklabels(), visible=False)
plt.title('Difference')
# Cumulative impact
ax3 = plt.subplot(grid[-1, :], sharex=ax1)
plt.plot(self.data.index,
self.result['cum_impact'],
'r--',
linewidth=2)
plt.plot(self.data.index,
np.zeros(self.data.shape[0]),
'g-',
linewidth=2)
plt.axvline(self._inter_index, c='k', linestyle='--')
plt.fill_between(
self.data.index,
self.result['cum_impact_conf_int_lower'],
self.result['cum_impact_conf_int_upper'],
facecolor='gray',
interpolate=True,
alpha=0.25,
)
plt.axis([self.data.index[0], self.data.index[-1], None, None])
ax3.set_xticklabels(self._input_index, rotation=45)
plt.locator_params(axis='x', nbins=min(12, self.data.shape[0]))
plt.title('Cumulative Impact')
plt.xlabel('$T$')
plt.show()