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test_sarimax.py
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test_sarimax.py
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"""
Tests for SARIMAX models
Author: Chad Fulton
License: Simplified-BSD
"""
import os
import warnings
from statsmodels.compat.platform import PLATFORM_WIN
import numpy as np
import pandas as pd
import pytest
from statsmodels.tsa.statespace import sarimax, tools
from .results import results_sarimax
from statsmodels.tools import add_constant
from statsmodels.tools.tools import Bunch
from numpy.testing import (
assert_, assert_equal, assert_almost_equal, assert_raises, assert_allclose
)
current_path = os.path.dirname(os.path.abspath(__file__))
realgdp_path = os.path.join('results', 'results_realgdpar_stata.csv')
realgdp_results = pd.read_csv(current_path + os.sep + realgdp_path)
coverage_path = os.path.join('results', 'results_sarimax_coverage.csv')
coverage_results = pd.read_csv(os.path.join(current_path, coverage_path))
class TestSARIMAXStatsmodels(object):
"""
Test ARIMA model using SARIMAX class against statsmodels ARIMA class
Notes
-----
Standard errors are quite good for the OPG case.
"""
@classmethod
def setup_class(cls):
cls.true = results_sarimax.wpi1_stationary
endog = cls.true['data']
# Old results from statsmodels.arima.ARIMA taken before it was removed
# to let test continue to run. On old statsmodels, can run
# result_a = arima.ARIMA(endog, order=(1, 1, 1)).fit(disp=-1)
result_a = Bunch()
result_a.llf = -135.3513139733829
result_a.aic = 278.7026279467658
result_a.bic = 289.9513653682555
result_a.hqic = 283.27183681851653
result_a.params = np.array([ 0.74982449, 0.87421135, -0.41202195])
result_a.bse = np.array([0.29207409, 0.06377779, 0.12208469])
cls.result_a = result_a
cls.model_b = sarimax.SARIMAX(endog, order=(1, 1, 1), trend='c',
simple_differencing=True,
hamilton_representation=True)
cls.result_b = cls.model_b.fit(disp=-1)
def test_loglike(self):
assert_allclose(self.result_b.llf, self.result_a.llf)
def test_aic(self):
assert_allclose(self.result_b.aic, self.result_a.aic)
def test_bic(self):
assert_allclose(self.result_b.bic, self.result_a.bic)
def test_hqic(self):
assert_allclose(self.result_b.hqic, self.result_a.hqic)
def test_mle(self):
# ARIMA estimates the mean of the process, whereas SARIMAX estimates
# the intercept. Convert the mean to intercept to compare
params_a = self.result_a.params.copy()
params_a[0] = (1 - params_a[1]) * params_a[0]
assert_allclose(self.result_b.params[:-1], params_a, atol=5e-5)
def test_bse(self):
# Test the complex step approximated BSE values
cpa = self.result_b._cov_params_approx(approx_complex_step=True)
bse = cpa.diagonal()**0.5
assert_allclose(bse[1:-1], self.result_a.bse[1:], atol=1e-5)
def test_t_test(self):
import statsmodels.tools._testing as smt
# to trigger failure, un-comment the following:
# self.result_b._cache['pvalues'] += 1
smt.check_ttest_tvalues(self.result_b)
smt.check_ftest_pvalues(self.result_b)
class TestRealGDPARStata(object):
"""
Includes tests of filtered states and standardized forecast errors.
Notes
-----
Could also test the usual things like standard errors, etc. but those are
well-tested elsewhere.
"""
@classmethod
def setup_class(cls):
dlgdp = np.log(realgdp_results['value']).diff()[1:].values
cls.model = sarimax.SARIMAX(dlgdp, order=(12, 0, 0), trend='n',
hamilton_representation=True)
# Estimated by Stata
params = [
.40725515, .18782621, -.01514009, -.01027267, -.03642297,
.11576416, .02573029, -.00766572, .13506498, .08649569, .06942822,
-.10685783, .00007999607
]
cls.results = cls.model.filter(params)
def test_filtered_state(self):
for i in range(12):
assert_allclose(
realgdp_results.iloc[1:]['u%d' % (i+1)],
self.results.filter_results.filtered_state[i],
atol=1e-6
)
def test_standardized_forecasts_error(self):
assert_allclose(
realgdp_results.iloc[1:]['rstd'],
self.results.filter_results.standardized_forecasts_error[0],
atol=1e-3
)
class SARIMAXStataTests(object):
def test_loglike(self):
assert_almost_equal(
self.result.llf,
self.true['loglike'], 4
)
def test_aic(self):
assert_almost_equal(
self.result.aic,
self.true['aic'], 3
)
def test_bic(self):
assert_almost_equal(
self.result.bic,
self.true['bic'], 3
)
def test_hqic(self):
hqic = (
-2*self.result.llf +
2*np.log(np.log(self.result.nobs_effective)) *
self.result.params.shape[0]
)
assert_almost_equal(
self.result.hqic,
hqic, 3
)
def test_standardized_forecasts_error(self):
cython_sfe = self.result.standardized_forecasts_error
self.result._standardized_forecasts_error = None
python_sfe = self.result.standardized_forecasts_error
assert_allclose(cython_sfe, python_sfe)
class ARIMA(SARIMAXStataTests):
"""
ARIMA model
Stata arima documentation, Example 1
"""
@classmethod
def setup_class(cls, true, *args, **kwargs):
cls.true = true
endog = true['data']
kwargs.setdefault('simple_differencing', True)
kwargs.setdefault('hamilton_representation', True)
cls.model = sarimax.SARIMAX(endog, order=(1, 1, 1), trend='c',
*args, **kwargs)
# Stata estimates the mean of the process, whereas SARIMAX estimates
# the intercept of the process. Get the intercept.
intercept = (1 - true['params_ar'][0]) * true['params_mean'][0]
params = np.r_[intercept, true['params_ar'], true['params_ma'],
true['params_variance']]
cls.result = cls.model.filter(params)
def test_mle(self):
result = self.model.fit(disp=-1)
assert_allclose(
result.params, self.result.params,
atol=1e-3
)
class TestARIMAStationary(ARIMA):
"""
Notes
-----
Standard errors are very good for the OPG and complex step approximation
cases.
"""
@classmethod
def setup_class(cls):
super(TestARIMAStationary, cls).setup_class(
results_sarimax.wpi1_stationary
)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[1], self.true['se_ar_opg'], atol=1e-7)
assert_allclose(self.result.bse[2], self.true['se_ma_opg'], atol=1e-7)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-7)
assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-7)
# The below tests pass irregularly; they give a sense of the precision
# available with finite differencing
# finite difference, non-centered
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2)
# assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-1)
# # finite difference, centered
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-3)
# assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-3)
def test_bse_oim(self):
# OIM covariance type
oim_bse = self.result.cov_params_oim.diagonal()**0.5
assert_allclose(oim_bse[1], self.true['se_ar_oim'], atol=1e-3)
assert_allclose(oim_bse[2], self.true['se_ma_oim'], atol=1e-2)
def test_bse_robust(self):
robust_oim_bse = self.result.cov_params_robust_oim.diagonal()**0.5
cpra = self.result.cov_params_robust_approx
robust_approx_bse = cpra.diagonal()**0.5
true_robust_bse = np.r_[
self.true['se_ar_robust'], self.true['se_ma_robust']
]
assert_allclose(robust_oim_bse[1:3], true_robust_bse, atol=1e-2)
assert_allclose(robust_approx_bse[1:3], true_robust_bse, atol=1e-3)
class TestARIMADiffuse(ARIMA):
"""
Notes
-----
Standard errors are very good for the OPG and quite good for the complex
step approximation cases.
"""
@classmethod
def setup_class(cls, **kwargs):
kwargs['initialization'] = 'approximate_diffuse'
kwargs['initial_variance'] = (
results_sarimax.wpi1_diffuse['initial_variance']
)
super(TestARIMADiffuse, cls).setup_class(results_sarimax.wpi1_diffuse,
**kwargs)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[1], self.true['se_ar_opg'], atol=1e-7)
assert_allclose(self.result.bse[2], self.true['se_ma_opg'], atol=1e-7)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4)
assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-4)
# The below tests do not pass
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered : failure
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4)
# assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-4)
# # finite difference, centered : failure
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4)
# assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-4)
def test_bse_oim(self):
# OIM covariance type
bse = self.result._cov_params_oim().diagonal()**0.5
assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2)
assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-1)
class AdditiveSeasonal(SARIMAXStataTests):
"""
ARIMA model with additive seasonal effects
Stata arima documentation, Example 2
"""
@classmethod
def setup_class(cls, true, *args, **kwargs):
cls.true = true
endog = np.log(true['data'])
kwargs.setdefault('simple_differencing', True)
kwargs.setdefault('hamilton_representation', True)
cls.model = sarimax.SARIMAX(
endog, order=(1, 1, (1, 0, 0, 1)), trend='c', *args, **kwargs
)
# Stata estimates the mean of the process, whereas SARIMAX estimates
# the intercept of the process. Get the intercept.
intercept = (1 - true['params_ar'][0]) * true['params_mean'][0]
params = np.r_[intercept, true['params_ar'], true['params_ma'],
true['params_variance']]
cls.result = cls.model.filter(params)
def test_mle(self):
result = self.model.fit(disp=-1)
assert_allclose(
result.params, self.result.params,
atol=1e-3
)
class TestAdditiveSeasonal(AdditiveSeasonal):
"""
Notes
-----
Standard errors are very good for the OPG and quite good for the complex
step approximation cases.
"""
@classmethod
def setup_class(cls):
super(TestAdditiveSeasonal, cls).setup_class(
results_sarimax.wpi1_seasonal
)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[1], self.true['se_ar_opg'], atol=1e-6)
assert_allclose(self.result.bse[2:4], self.true['se_ma_opg'],
atol=1e-5)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4)
assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-4)
# The below tests pass irregularly; they give a sense of the precision
# available with finite differencing
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2)
# assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-2)
# # finite difference, centered
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-3)
# assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-3)
def test_bse_oim(self):
# OIM covariance type
bse = self.result._cov_params_oim().diagonal()**0.5
assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2)
assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-1)
class Airline(SARIMAXStataTests):
"""
Multiplicative SARIMA model: "Airline" model
Stata arima documentation, Example 3
"""
@classmethod
def setup_class(cls, true, *args, **kwargs):
cls.true = true
endog = np.log(true['data'])
kwargs.setdefault('simple_differencing', True)
kwargs.setdefault('hamilton_representation', True)
cls.model = sarimax.SARIMAX(
endog, order=(0, 1, 1), seasonal_order=(0, 1, 1, 12),
trend='n', *args, **kwargs
)
params = np.r_[true['params_ma'], true['params_seasonal_ma'],
true['params_variance']]
cls.result = cls.model.filter(params)
def test_mle(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore")
result = self.model.fit(disp=-1)
assert_allclose(
result.params, self.result.params,
atol=1e-4
)
class TestAirlineHamilton(Airline):
"""
Notes
-----
Standard errors are very good for the OPG and complex step approximation
cases.
"""
@classmethod
def setup_class(cls):
super(TestAirlineHamilton, cls).setup_class(
results_sarimax.air2_stationary
)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[0], self.true['se_ma_opg'], atol=1e-6)
assert_allclose(self.result.bse[1], self.true['se_seasonal_ma_opg'],
atol=1e-6)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-6)
assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], atol=1e-6)
# The below tests pass irregularly; they give a sense of the precision
# available with finite differencing
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-2)
# assert_allclose(bse[1], self.true['se_seasonal_ma_oim'],
# atol=1e-2)
# # finite difference, centered
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4)
# assert_allclose(bse[1], self.true['se_seasonal_ma_oim'],
# atol=1e-4)
def test_bse_oim(self):
# OIM covariance type
oim_bse = self.result.cov_params_oim.diagonal()**0.5
assert_allclose(oim_bse[0], self.true['se_ma_oim'], atol=1e-1)
assert_allclose(oim_bse[1], self.true['se_seasonal_ma_oim'], atol=1e-1)
class TestAirlineHarvey(Airline):
"""
Notes
-----
Standard errors are very good for the OPG and complex step approximation
cases.
"""
@classmethod
def setup_class(cls):
super(TestAirlineHarvey, cls).setup_class(
results_sarimax.air2_stationary, hamilton_representation=False
)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[0], self.true['se_ma_opg'], atol=1e-6)
assert_allclose(self.result.bse[1], self.true['se_seasonal_ma_opg'],
atol=1e-6)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-6)
assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], atol=1e-6)
# The below tests pass irregularly; they give a sense of the precision
# available with finite differencing
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-2)
# assert_allclose(bse[1], self.true['se_seasonal_ma_oim'],
# atol=1e-2)
# # finite difference, centered
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4)
# assert_allclose(bse[1], self.true['se_seasonal_ma_oim'],
# atol=1e-4)
def test_bse_oim(self):
# OIM covariance type
oim_bse = self.result.cov_params_oim.diagonal()**0.5
assert_allclose(oim_bse[0], self.true['se_ma_oim'], atol=1e-1)
assert_allclose(oim_bse[1], self.true['se_seasonal_ma_oim'], atol=1e-1)
class TestAirlineStateDifferencing(Airline):
"""
Notes
-----
Standard errors are very good for the OPG and quite good for the complex
step approximation cases.
"""
@classmethod
def setup_class(cls):
super(TestAirlineStateDifferencing, cls).setup_class(
results_sarimax.air2_stationary, simple_differencing=False,
hamilton_representation=False
)
def test_bic(self):
# Due to diffuse component of the state (which technically changes the
# BIC calculation - see Durbin and Koopman section 7.4), this is the
# best we can do for BIC
assert_almost_equal(
self.result.bic,
self.true['bic'], 0
)
def test_mle(self):
result = self.model.fit(method='nm', maxiter=1000, disp=0)
assert_allclose(
result.params, self.result.params,
atol=1e-3)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[0], self.true['se_ma_opg'], atol=1e-6)
assert_allclose(self.result.bse[1], self.true['se_seasonal_ma_opg'],
atol=1e-6)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4)
assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], atol=1e-4)
# The below tests do not pass
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered : failure with NaNs
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-2)
# assert_allclose(bse[1], self.true['se_seasonal_ma_oim'],
# atol=1e-2)
# # finite difference, centered : failure with NaNs
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4)
# assert_allclose(bse[1], self.true['se_seasonal_ma_oim'],
# atol=1e-4)
def test_bse_oim(self):
# OIM covariance type
oim_bse = self.result.cov_params_oim.diagonal()**0.5
assert_allclose(oim_bse[0], self.true['se_ma_oim'], atol=1e-1)
assert_allclose(oim_bse[1], self.true['se_seasonal_ma_oim'], atol=1e-1)
class Friedman(SARIMAXStataTests):
"""
ARMAX model: Friedman quantity theory of money
Stata arima documentation, Example 4
"""
@classmethod
def setup_class(cls, true, exog=None, *args, **kwargs):
cls.true = true
endog = np.r_[true['data']['consump']]
if exog is None:
exog = add_constant(true['data']['m2'])
kwargs.setdefault('simple_differencing', True)
kwargs.setdefault('hamilton_representation', True)
cls.model = sarimax.SARIMAX(
endog, exog=exog, order=(1, 0, 1), *args, **kwargs
)
params = np.r_[true['params_exog'], true['params_ar'],
true['params_ma'], true['params_variance']]
cls.result = cls.model.filter(params)
class TestFriedmanMLERegression(Friedman):
"""
Notes
-----
Standard errors are very good for the OPG and complex step approximation
cases.
"""
@classmethod
def setup_class(cls):
super(TestFriedmanMLERegression, cls).setup_class(
results_sarimax.friedman2_mle
)
def test_mle(self):
result = self.model.fit(disp=-1)
# Use ratio to make atol more meaningful parameter scale differs
ratio = result.params / self.result.params
assert_allclose(ratio, np.ones(5), atol=1e-2, rtol=1e-3)
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[0:2], self.true['se_exog_opg'],
atol=1e-4)
assert_allclose(self.result.bse[2], self.true['se_ar_opg'], atol=1e-6)
assert_allclose(self.result.bse[3], self.true['se_ma_opg'], atol=1e-6)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[0:2], self.true['se_exog_oim'], atol=1e-4)
assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-6)
assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-6)
# The below tests pass irregularly; they give a sense of the precision
# available with finite differencing
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[0], self.true['se_exog_oim'][0], rtol=1)
# assert_allclose(bse[1], self.true['se_exog_oim'][1], atol=1e-2)
# assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-2)
# assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-2)
# # finite difference, centered
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[0], self.true['se_exog_oim'][0], rtol=1)
# assert_allclose(bse[1], self.true['se_exog_oim'][1], atol=1e-2)
# assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-2)
# assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-2)
def test_bse_oim(self):
# OIM covariance type
bse = self.result.cov_params_oim.diagonal()**0.5
assert_allclose(bse[0], self.true['se_exog_oim'][0], rtol=1)
assert_allclose(bse[1], self.true['se_exog_oim'][1], atol=1e-2)
assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-2)
assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-2)
class TestFriedmanStateRegression(Friedman):
"""
Notes
-----
MLE is not very close and standard errors are not very close for any set of
parameters.
This is likely because we're comparing against the model where the
regression coefficients are also estimated by MLE. So this test should be
considered just a very basic "sanity" test.
"""
@classmethod
def setup_class(cls):
# Remove the regression coefficients from the parameters, since they
# will be estimated as part of the state vector
true = dict(results_sarimax.friedman2_mle)
exog = add_constant(true['data']['m2']) / 10.
true['mle_params_exog'] = true['params_exog'][:]
true['mle_se_exog'] = true['se_exog_opg'][:]
true['params_exog'] = []
true['se_exog'] = []
super(TestFriedmanStateRegression, cls).setup_class(
true, exog=exog, mle_regression=False
)
cls.true_params = np.r_[true['params_exog'], true['params_ar'],
true['params_ma'], true['params_variance']]
cls.result = cls.model.filter(cls.true_params)
def test_mle(self):
result = self.model.fit(disp=-1)
assert_allclose(
result.params, self.result.params,
atol=1e-1, rtol=2e-1
)
def test_regression_parameters(self):
# The regression effects are integrated into the state vector as
# the last two states (thus the index [-2:]). The filtered
# estimates of the state vector produced by the Kalman filter and
# stored in `filtered_state` for these state elements give the
# recursive least squares estimates of the regression coefficients
# at each time period. To get the estimates conditional on the
# entire dataset, use the filtered states from the last time
# period (thus the index [-1]).
assert_almost_equal(
self.result.filter_results.filtered_state[-2:, -1] / 10.,
self.true['mle_params_exog'], 1
)
# Loglikelihood (and so aic, bic) is slightly different when states are
# integrated into the state vector
def test_loglike(self):
pass
def test_aic(self):
pass
def test_bic(self):
pass
def test_bse(self):
# test defaults
assert_equal(self.result.cov_type, 'opg')
assert_equal(self.result._cov_approx_complex_step, True)
assert_equal(self.result._cov_approx_centered, False)
# default covariance type (opg)
assert_allclose(self.result.bse[0], self.true['se_ar_opg'], atol=1e-2)
assert_allclose(self.result.bse[1], self.true['se_ma_opg'], atol=1e-2)
def test_bse_approx(self):
# complex step
bse = self.result._cov_params_approx(
approx_complex_step=True).diagonal()**0.5
assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-1)
assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-1)
# The below tests do not pass
# with warnings.catch_warnings():
# warnings.simplefilter("ignore")
# # finite difference, non-centered :
# # failure (catastrophic cancellation)
# bse = self.result._cov_params_approx(
# approx_complex_step=False).diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-3)
# assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-2)
# # finite difference, centered : failure (nan)
# cpa = self.result._cov_params_approx(
# approx_complex_step=False, approx_centered=True)
# bse = cpa.diagonal()**0.5
# assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-3)
# assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-3)
def test_bse_oim(self):
# OIM covariance type
bse = self.result._cov_params_oim().diagonal()**0.5
assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-1)
assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-1)
class TestFriedmanPredict(Friedman):
"""
ARMAX model: Friedman quantity theory of money, prediction
Stata arima postestimation documentation, Example 1 - Dynamic forecasts
This follows the given Stata example, although it is not truly forecasting
because it compares using the actual data (which is available in the
example but just not used in the parameter MLE estimation) against dynamic
prediction of that data. Here `test_predict` matches the first case, and
`test_dynamic_predict` matches the second.
"""
@classmethod
def setup_class(cls):
super(TestFriedmanPredict, cls).setup_class(
results_sarimax.friedman2_predict
)
# loglike, aic, bic are not the point of this test (they could pass, but we
# would have to modify the data so that they were calculated to
# exclude the last 15 observations)
def test_loglike(self):
pass
def test_aic(self):
pass
def test_bic(self):
pass
def test_predict(self):
assert_almost_equal(
self.result.predict(),
self.true['predict'], 3
)
def test_dynamic_predict(self):
dynamic = len(self.true['data']['consump'])-15-1
assert_almost_equal(
self.result.predict(dynamic=dynamic),
self.true['dynamic_predict'], 3
)
class TestFriedmanForecast(Friedman):
"""
ARMAX model: Friedman quantity theory of money, forecasts
Variation on:
Stata arima postestimation documentation, Example 1 - Dynamic forecasts
This is a variation of the Stata example, in which the endogenous data is
actually made to be missing so that the predict command must forecast.
As another unit test, we also compare against the case in State when
predict is used against missing data (so forecasting) with the dynamic
option also included. Note, however, that forecasting in State space models
amounts to running the Kalman filter against missing datapoints, so it is
not clear whether "dynamic" forecasting (where instead of missing
datapoints for lags, we plug in previous forecasted endog values) is
meaningful.
"""
@classmethod
def setup_class(cls):
true = dict(results_sarimax.friedman2_predict)
true['forecast_data'] = {
'consump': true['data']['consump'][-15:],
'm2': true['data']['m2'][-15:]
}
true['data'] = {
'consump': true['data']['consump'][:-15],
'm2': true['data']['m2'][:-15]
}
super(TestFriedmanForecast, cls).setup_class(true)
cls.result = cls.model.filter(cls.result.params)
# loglike, aic, bic are not the point of this test (they could pass, but we
# would have to modify the data so that they were calculated to
# exclude the last 15 observations)
def test_loglike(self):
pass
def test_aic(self):
pass
def test_bic(self):
pass
def test_forecast(self):
end = len(self.true['data']['consump'])+15-1
exog = add_constant(self.true['forecast_data']['m2'])
assert_almost_equal(
self.result.predict(end=end, exog=exog),
self.true['forecast'], 3
)
def test_dynamic_forecast(self):
end = len(self.true['data']['consump'])+15-1
dynamic = len(self.true['data']['consump'])-1
exog = add_constant(self.true['forecast_data']['m2'])
assert_almost_equal(
self.result.predict(end=end, dynamic=dynamic, exog=exog),
self.true['dynamic_forecast'], 3
)
class SARIMAXCoverageTest(object):
@classmethod
def setup_class(cls, i, decimal=4, endog=None, *args, **kwargs):
# Dataset
if endog is None:
endog = results_sarimax.wpi1_data
# Loglikelihood, parameters
cls.true_loglike = coverage_results.loc[i]['llf']
cls.true_params = np.array([
float(x) for x in coverage_results.loc[i]['parameters'].split(',')]
)
# Stata reports the standard deviation; make it the variance
cls.true_params[-1] = cls.true_params[-1]**2
# Test parameters
cls.decimal = decimal
# Compare using the Hamilton representation and simple differencing
kwargs.setdefault('simple_differencing', True)
kwargs.setdefault('hamilton_representation', True)
cls.model = sarimax.SARIMAX(endog, *args, **kwargs)
def test_loglike(self):
self.result = self.model.filter(self.true_params)
assert_allclose(
self.result.llf,
self.true_loglike,
atol=0.7 * 10**(-self.decimal)
)
def test_start_params(self):
# just a quick test that start_params is not throwing an exception
# (other than related to invertibility)
stat = self.model.enforce_stationarity
inv = self.model.enforce_invertibility
self.model.enforce_stationarity = False
self.model.enforce_invertibility = False
self.model.start_params
self.model.enforce_stationarity = stat
self.model.enforce_invertibility = inv
def test_transform_untransform(self):
model = self.model
stat, inv = model.enforce_stationarity, model.enforce_invertibility
true_constrained = self.true_params