some new features
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ilgazca
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|
||||
.3807178,.6192821,.3201608,.6798392,.1632341,.8367659,-.1369031,.2466296,.1006118,.1238374,.7574543
|
||||
.3643857,.6356143,.0228407,.9771593,.0520427,.9479573,-.4943302,.9059532,.3957099,.8739698,.9687712
|
||||
.3570154,.6429846,.0027989,.9972011,.0035125,.9964876,-.2296742,1.026684,.5781449,1.023168,1.395377
|
||||
.3565186,.6434814,.1375207,.8624793,.1369265,.8630735,.132511,1.19744,.8177727,1.05099,1.492269
|
||||
.3598582,.6401418,.2749309,.7250692,.6349947,.3650052,.3607773,.7020003,.5792084,.6081876,.8663656
|
||||
.3632645,.6367355,.0747665,.9252335,.04608,.9539199,.2392728,.9091664,.6658179,.8590808,1.638283
|
||||
.3583026,.6416974,.3430003,.6569996,.2439876,.7560124,.3945461,1.222072,.9255675,.9382305,1.486441
|
||||
.3649519,.6350481,.2784336,.7215664,.2026928,.7973073,.5596761,.5065153,.5259164,.521317,.917065
|
||||
.3633513,.6366487,.4820935,.5179065,.4820935,.5179065,.0647946,.6038795,.4080022,.3439901,.4402459
|
||||
|
@ -0,0 +1,905 @@
|
||||
"""
|
||||
Tests for Markov Autoregression models
|
||||
|
||||
Author: Chad Fulton
|
||||
License: BSD-3
|
||||
"""
|
||||
|
||||
import warnings
|
||||
import os
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_equal, assert_allclose
|
||||
import pandas as pd
|
||||
import pytest
|
||||
|
||||
from statsmodels.tools import add_constant
|
||||
from statsmodels.tsa.regime_switching import markov_autoregression
|
||||
|
||||
current_path = os.path.dirname(os.path.abspath(__file__))
|
||||
|
||||
|
||||
rgnp = [2.59316421, 2.20217133, 0.45827562, 0.9687438,
|
||||
-0.24130757, 0.89647478, 2.05393219, 1.73353648,
|
||||
0.93871289, -0.46477833, -0.80983406, -1.39763689,
|
||||
-0.39886093, 1.1918416, 1.45620048, 2.11808228,
|
||||
1.08957863, 1.32390273, 0.87296367, -0.19773273,
|
||||
0.45420215, 0.07221876, 1.1030364, 0.82097489,
|
||||
-0.05795795, 0.58447772, -1.56192672, -2.05041027,
|
||||
0.53637183, 2.33676839, 2.34014559, 1.2339263,
|
||||
1.8869648, -0.45920792, 0.84940469, 1.70139849,
|
||||
-0.28756312, 0.09594627, -0.86080289, 1.03447127,
|
||||
1.23685944, 1.42004502, 2.22410631, 1.30210173,
|
||||
1.03517699, 0.9253425, -0.16559951, 1.3444382,
|
||||
1.37500131, 1.73222184, 0.71605635, 2.21032143,
|
||||
0.85333031, 1.00238776, 0.42725441, 2.14368343,
|
||||
1.43789184, 1.57959926, 2.27469826, 1.95962656,
|
||||
0.25992399, 1.01946914, 0.49016398, 0.5636338,
|
||||
0.5959546, 1.43082857, 0.56230122, 1.15388393,
|
||||
1.68722844, 0.77438205, -0.09647045, 1.39600146,
|
||||
0.13646798, 0.55223715, -0.39944872, -0.61671102,
|
||||
-0.08722561, 1.2101835, -0.90729755, 2.64916158,
|
||||
-0.0080694, 0.51111895, -0.00401437, 2.16821432,
|
||||
1.92586732, 1.03504717, 1.85897219, 2.32004929,
|
||||
0.25570789, -0.09855274, 0.89073682, -0.55896485,
|
||||
0.28350255, -1.31155407, -0.88278776, -1.97454941,
|
||||
1.01275265, 1.68264723, 1.38271284, 1.86073637,
|
||||
0.4447377, 0.41449001, 0.99202275, 1.36283576,
|
||||
1.59970522, 1.98845816, -0.25684232, 0.87786949,
|
||||
3.1095655, 0.85324478, 1.23337317, 0.00314302,
|
||||
-0.09433369, 0.89883322, -0.19036628, 0.99772376,
|
||||
-2.39120054, 0.06649673, 1.26136017, 1.91637838,
|
||||
-0.3348029, 0.44207108, -1.40664911, -1.52129889,
|
||||
0.29919869, -0.80197448, 0.15204792, 0.98585027,
|
||||
2.13034606, 1.34397924, 1.61550522, 2.70930099,
|
||||
1.24461412, 0.50835466, 0.14802167]
|
||||
|
||||
rec = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
|
||||
1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
||||
1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]
|
||||
|
||||
|
||||
def test_predict():
|
||||
# AR(1) without mean, k_regimes=2
|
||||
endog = np.ones(10)
|
||||
markov_autoregression.MarkovAutoregression(
|
||||
endog,
|
||||
k_regimes=2,
|
||||
order=1,
|
||||
trend='n'
|
||||
)
|
||||
mod = markov_autoregression.MarkovAutoregression(
|
||||
endog, k_regimes=2, order=1, trend='n')
|
||||
assert_equal(mod.nobs, 9)
|
||||
assert_equal(mod.endog, np.ones(9))
|
||||
|
||||
params = np.r_[0.5, 0.5, 1., 0.1, 0.5]
|
||||
mod_resid = mod._resid(params)
|
||||
resids = np.zeros((2, 2, mod.nobs))
|
||||
# Resids when: S_{t} = 0
|
||||
resids[0, :, :] = np.ones(9) - 0.1 * np.ones(9)
|
||||
assert_allclose(mod_resid[0, :, :], resids[0, :, :])
|
||||
# Resids when: S_{t} = 1
|
||||
resids[1, :, :] = np.ones(9) - 0.5 * np.ones(9)
|
||||
assert_allclose(mod_resid[1, :, :], resids[1, :, :])
|
||||
|
||||
# AR(1) with mean, k_regimes=2
|
||||
endog = np.arange(10)
|
||||
mod = markov_autoregression.MarkovAutoregression(
|
||||
endog, k_regimes=2, order=1)
|
||||
assert_equal(mod.nobs, 9)
|
||||
assert_equal(mod.endog, np.arange(1, 10))
|
||||
|
||||
params = np.r_[0.5, 0.5, 2., 3., 1., 0.1, 0.5]
|
||||
mod_resid = mod._resid(params)
|
||||
resids = np.zeros((2, 2, mod.nobs))
|
||||
# Resids when: S_t = 0, S_{t-1} = 0
|
||||
resids[0, 0, :] = (np.arange(1, 10) - 2.) - 0.1 * (np.arange(9) - 2.)
|
||||
assert_allclose(mod_resid[0, 0, :], resids[0, 0, :])
|
||||
# Resids when: S_t = 0, S_{t-1} = 1
|
||||
resids[0, 1, :] = (np.arange(1, 10) - 2.) - 0.1 * (np.arange(9) - 3.)
|
||||
assert_allclose(mod_resid[0, 1, :], resids[0, 1, :])
|
||||
# Resids when: S_t = 1, S_{t-1} = 0
|
||||
resids[1, 0, :] = (np.arange(1, 10) - 3.) - 0.5 * (np.arange(9) - 2.)
|
||||
assert_allclose(mod_resid[1, 0, :], resids[1, 0, :])
|
||||
# Resids when: S_t = 1, S_{t-1} = 1
|
||||
resids[1, 1, :] = (np.arange(1, 10) - 3.) - 0.5 * (np.arange(9) - 3.)
|
||||
assert_allclose(mod_resid[1, 1, :], resids[1, 1, :])
|
||||
|
||||
# AR(2) with mean, k_regimes=3
|
||||
endog = np.arange(10)
|
||||
mod = markov_autoregression.MarkovAutoregression(
|
||||
endog, k_regimes=3, order=2)
|
||||
assert_equal(mod.nobs, 8)
|
||||
assert_equal(mod.endog, np.arange(2, 10))
|
||||
|
||||
params = np.r_[[0.3] * 6, 2., 3., 4, 1., 0.1, 0.5, 0.8, -0.05, -0.25, -0.4]
|
||||
mod_resid = mod._resid(params)
|
||||
resids = np.zeros((3, 3, 3, mod.nobs))
|
||||
# Resids when: S_t = 0, S_{t-1} = 0, S_{t-2} = 0
|
||||
resids[0, 0, 0, :] = (
|
||||
(np.arange(2, 10) - 2.) -
|
||||
0.1 * (np.arange(1, 9) - 2.) -
|
||||
(-0.05) * (np.arange(8) - 2.))
|
||||
assert_allclose(mod_resid[0, 0, 0, :], resids[0, 0, 0, :])
|
||||
|
||||
# Resids when: S_t = 1, S_{t-1} = 0, S_{t-2} = 0
|
||||
resids[1, 0, 0, :] = (
|
||||
(np.arange(2, 10) - 3.) -
|
||||
0.5 * (np.arange(1, 9) - 2.) -
|
||||
(-0.25) * (np.arange(8) - 2.))
|
||||
assert_allclose(mod_resid[1, 0, 0, :], resids[1, 0, 0, :])
|
||||
|
||||
# Resids when: S_t = 0, S_{t-1} = 2, S_{t-2} = 1
|
||||
resids[0, 2, 1, :] = (
|
||||
(np.arange(2, 10) - 2.) -
|
||||
0.1 * (np.arange(1, 9) - 4.) -
|
||||
(-0.05) * (np.arange(8) - 3.))
|
||||
assert_allclose(mod_resid[0, 2, 1, :], resids[0, 2, 1, :])
|
||||
|
||||
# AR(1) with mean + non-switching exog
|
||||
endog = np.arange(10)
|
||||
exog = np.r_[0.4, 5, 0.2, 1.2, -0.3, 2.5, 0.2, -0.7, 2., -1.1]
|
||||
mod = markov_autoregression.MarkovAutoregression(
|
||||
endog, k_regimes=2, order=1, exog=exog)
|
||||
assert_equal(mod.nobs, 9)
|
||||
assert_equal(mod.endog, np.arange(1, 10))
|
||||
|
||||
params = np.r_[0.5, 0.5, 2., 3., 1.5, 1., 0.1, 0.5]
|
||||
mod_resid = mod._resid(params)
|
||||
resids = np.zeros((2, 2, mod.nobs))
|
||||
# Resids when: S_t = 0, S_{t-1} = 0
|
||||
resids[0, 0, :] = (
|
||||
(np.arange(1, 10) - 2. - 1.5 * exog[1:]) -
|
||||
0.1 * (np.arange(9) - 2. - 1.5 * exog[:-1]))
|
||||
assert_allclose(mod_resid[0, 0, :], resids[0, 0, :])
|
||||
# Resids when: S_t = 0, S_{t-1} = 1
|
||||
resids[0, 1, :] = (
|
||||
(np.arange(1, 10) - 2. - 1.5 * exog[1:]) -
|
||||
0.1 * (np.arange(9) - 3. - 1.5 * exog[:-1]))
|
||||
assert_allclose(mod_resid[0, 1, :], resids[0, 1, :])
|
||||
# Resids when: S_t = 1, S_{t-1} = 0
|
||||
resids[1, 0, :] = (
|
||||
(np.arange(1, 10) - 3. - 1.5 * exog[1:]) -
|
||||
0.5 * (np.arange(9) - 2. - 1.5 * exog[:-1]))
|
||||
assert_allclose(mod_resid[1, 0, :], resids[1, 0, :])
|
||||
# Resids when: S_t = 1, S_{t-1} = 1
|
||||
resids[1, 1, :] = (
|
||||
(np.arange(1, 10) - 3. - 1.5 * exog[1:]) -
|
||||
0.5 * (np.arange(9) - 3. - 1.5 * exog[:-1]))
|
||||
assert_allclose(mod_resid[1, 1, :], resids[1, 1, :])
|
||||
|
||||
|
||||
def test_conditional_loglikelihoods():
|
||||
# AR(1) without mean, k_regimes=2, non-switching variance
|
||||
endog = np.ones(10)
|
||||
mod = markov_autoregression.MarkovAutoregression(
|
||||
endog, k_regimes=2, order=1)
|
||||
assert_equal(mod.nobs, 9)
|
||||
assert_equal(mod.endog, np.ones(9))
|
||||
|
||||
params = np.r_[0.5, 0.5, 2., 3., 2., 0.1, 0.5]
|
||||
resid = mod._resid(params)
|
||||
conditional_likelihoods = (
|
||||
np.exp(-0.5 * resid**2 / 2) / np.sqrt(2 * np.pi * 2))
|
||||
assert_allclose(mod._conditional_loglikelihoods(params),
|
||||
np.log(conditional_likelihoods))
|
||||
|
||||
# AR(1) without mean, k_regimes=3, switching variance
|
||||
endog = np.ones(10)
|
||||
mod = markov_autoregression.MarkovAutoregression(
|
||||
endog, k_regimes=3, order=1, switching_variance=True)
|
||||
assert_equal(mod.nobs, 9)
|
||||
assert_equal(mod.endog, np.ones(9))
|
||||
|
||||
params = np.r_[[0.3]*6, 2., 3., 4., 1.5, 3., 4.5, 0.1, 0.5, 0.8]
|
||||
mod_conditional_loglikelihoods = mod._conditional_loglikelihoods(params)
|
||||
conditional_likelihoods = mod._resid(params)
|
||||
|
||||
# S_t = 0
|
||||
conditional_likelihoods[0, :, :] = (
|
||||
np.exp(-0.5 * conditional_likelihoods[0, :, :]**2 / 1.5) /
|
||||
np.sqrt(2 * np.pi * 1.5))
|
||||
assert_allclose(mod_conditional_loglikelihoods[0, :, :],
|
||||
np.log(conditional_likelihoods[0, :, :]))
|
||||
# S_t = 1
|
||||
conditional_likelihoods[1, :, :] = (
|
||||
np.exp(-0.5 * conditional_likelihoods[1, :, :]**2 / 3.) /
|
||||
np.sqrt(2 * np.pi * 3.))
|
||||
assert_allclose(mod_conditional_loglikelihoods[1, :, :],
|
||||
np.log(conditional_likelihoods[1, :, :]))
|
||||
# S_t = 2
|
||||
conditional_likelihoods[2, :, :] = (
|
||||
np.exp(-0.5 * conditional_likelihoods[2, :, :]**2 / 4.5) /
|
||||
np.sqrt(2 * np.pi * 4.5))
|
||||
assert_allclose(mod_conditional_loglikelihoods[2, :, :],
|
||||
np.log(conditional_likelihoods[2, :, :]))
|
||||
|
||||
|
||||
class MarkovAutoregression:
|
||||
@classmethod
|
||||
def setup_class(cls, true, endog, atol=1e-5, rtol=1e-7, **kwargs):
|
||||
cls.model = markov_autoregression.MarkovAutoregression(endog, **kwargs)
|
||||
cls.true = true
|
||||
cls.result = cls.model.smooth(cls.true['params'])
|
||||
cls.atol = atol
|
||||
cls.rtol = rtol
|
||||
|
||||
def test_llf(self):
|
||||
assert_allclose(self.result.llf, self.true['llf'], atol=self.atol,
|
||||
rtol=self.rtol)
|
||||
|
||||
def test_fit(self, **kwargs):
|
||||
# Test fitting against Stata
|
||||
with warnings.catch_warnings():
|
||||
warnings.simplefilter("ignore")
|
||||
res = self.model.fit(disp=False, **kwargs)
|
||||
assert_allclose(res.llf, self.true['llf_fit'], atol=self.atol,
|
||||
rtol=self.rtol)
|
||||
|
||||
@pytest.mark.smoke
|
||||
def test_fit_em(self, **kwargs):
|
||||
# Test EM fitting (smoke test)
|
||||
res_em = self.model._fit_em(**kwargs)
|
||||
assert_allclose(res_em.llf, self.true['llf_fit_em'], atol=self.atol,
|
||||
rtol=self.rtol)
|
||||
|
||||
|
||||
hamilton_ar2_short_filtered_joint_probabilities = np.array([
|
||||
[[[4.99506987e-02, 6.44048275e-04, 6.22227140e-05,
|
||||
4.45756755e-06, 5.26645567e-07, 7.99846146e-07,
|
||||
1.19425705e-05, 6.87762063e-03],
|
||||
[1.95930395e-02, 3.25884335e-04, 1.12955091e-04,
|
||||
3.38537103e-04, 9.81927968e-06, 2.71696750e-05,
|
||||
5.83828290e-03, 7.64261509e-02]],
|
||||
|
||||
[[1.97113193e-03, 9.50372207e-05, 1.98390978e-04,
|
||||
1.88188953e-06, 4.83449400e-07, 1.14872860e-05,
|
||||
4.02918239e-06, 4.35015431e-04],
|
||||
[2.24870443e-02, 1.27331172e-03, 9.62155856e-03,
|
||||
4.04178695e-03, 2.75516282e-04, 1.18179572e-02,
|
||||
5.99778157e-02, 1.48149567e-01]]],
|
||||
|
||||
|
||||
[[[6.70912859e-02, 1.84223872e-02, 2.55621792e-04,
|
||||
4.48500688e-05, 7.80481515e-05, 2.73734559e-06,
|
||||
7.59835896e-06, 1.42930726e-03],
|
||||
[2.10053328e-02, 7.44036383e-03, 3.70388879e-04,
|
||||
2.71878370e-03, 1.16152088e-03, 7.42182691e-05,
|
||||
2.96490192e-03, 1.26774695e-02]],
|
||||
|
||||
[[8.09335679e-02, 8.31016518e-02, 2.49149080e-02,
|
||||
5.78825626e-04, 2.19019941e-03, 1.20179130e-03,
|
||||
7.83659430e-05, 2.76363377e-03],
|
||||
[7.36967899e-01, 8.88697316e-01, 9.64463954e-01,
|
||||
9.92270877e-01, 9.96283886e-01, 9.86863839e-01,
|
||||
9.31117063e-01, 7.51241236e-01]]]])
|
||||
|
||||
|
||||
hamilton_ar2_short_predicted_joint_probabilities = np.array([[
|
||||
[[[1.20809334e-01, 3.76964436e-02, 4.86045844e-04,
|
||||
4.69578023e-05, 3.36400588e-06, 3.97445190e-07,
|
||||
6.03622290e-07, 9.01273552e-06],
|
||||
[3.92723623e-02, 1.47863379e-02, 2.45936108e-04,
|
||||
8.52441571e-05, 2.55484811e-04, 7.41034525e-06,
|
||||
2.05042201e-05, 4.40599447e-03]],
|
||||
|
||||
[[4.99131230e-03, 1.48756005e-03, 7.17220245e-05,
|
||||
1.49720314e-04, 1.42021122e-06, 3.64846209e-07,
|
||||
8.66914462e-06, 3.04071516e-06],
|
||||
[4.70476003e-02, 1.69703652e-02, 9.60933974e-04,
|
||||
7.26113047e-03, 3.05022748e-03, 2.07924699e-04,
|
||||
8.91869322e-03, 4.52636381e-02]]],
|
||||
|
||||
|
||||
[[[4.99131230e-03, 6.43506069e-03, 1.76698327e-03,
|
||||
2.45179642e-05, 4.30179435e-06, 7.48598845e-06,
|
||||
2.62552503e-07, 7.28796600e-07],
|
||||
[1.62256192e-03, 2.01472650e-03, 7.13642497e-04,
|
||||
3.55258493e-05, 2.60772139e-04, 1.11407276e-04,
|
||||
7.11864528e-06, 2.84378568e-04]],
|
||||
|
||||
[[5.97950448e-03, 7.76274317e-03, 7.97069493e-03,
|
||||
2.38971340e-03, 5.55180599e-05, 2.10072977e-04,
|
||||
1.15269812e-04, 7.51646942e-06],
|
||||
[5.63621989e-02, 7.06862760e-02, 8.52394030e-02,
|
||||
9.25065601e-02, 9.51736612e-02, 9.55585689e-02,
|
||||
9.46550451e-02, 8.93080931e-02]]]],
|
||||
|
||||
|
||||
|
||||
[[[[3.92723623e-02, 1.22542551e-02, 1.58002431e-04,
|
||||
1.52649118e-05, 1.09356167e-06, 1.29200377e-07,
|
||||
1.96223855e-07, 2.92983500e-06],
|
||||
[1.27665503e-02, 4.80670161e-03, 7.99482261e-05,
|
||||
2.77109335e-05, 8.30522919e-05, 2.40893443e-06,
|
||||
6.66545485e-06, 1.43228843e-03]],
|
||||
|
||||
[[1.62256192e-03, 4.83571884e-04, 2.33151963e-05,
|
||||
4.86706634e-05, 4.61678312e-07, 1.18603191e-07,
|
||||
2.81814142e-06, 9.88467229e-07],
|
||||
[1.52941031e-02, 5.51667911e-03, 3.12377744e-04,
|
||||
2.36042810e-03, 9.91559466e-04, 6.75915830e-05,
|
||||
2.89926399e-03, 1.47141776e-02]]],
|
||||
|
||||
|
||||
[[[4.70476003e-02, 6.06562252e-02, 1.66554040e-02,
|
||||
2.31103828e-04, 4.05482745e-05, 7.05621631e-05,
|
||||
2.47479309e-06, 6.86956236e-06],
|
||||
[1.52941031e-02, 1.89906063e-02, 6.72672133e-03,
|
||||
3.34863029e-04, 2.45801156e-03, 1.05011361e-03,
|
||||
6.70996238e-05, 2.68052335e-03]],
|
||||
|
||||
[[5.63621989e-02, 7.31708248e-02, 7.51309569e-02,
|
||||
2.25251946e-02, 5.23307566e-04, 1.98012644e-03,
|
||||
1.08652148e-03, 7.08494735e-05],
|
||||
[5.31264334e-01, 6.66281623e-01, 8.03457913e-01,
|
||||
8.71957394e-01, 8.97097216e-01, 9.00725317e-01,
|
||||
8.92208794e-01, 8.41808970e-01]]]]])
|
||||
|
||||
|
||||
hamilton_ar2_short_smoothed_joint_probabilities = np.array([
|
||||
[[[1.29898189e-02, 1.66298475e-04, 1.29822987e-05,
|
||||
9.95268382e-07, 1.84473346e-07, 7.18761267e-07,
|
||||
1.69576494e-05, 6.87762063e-03],
|
||||
[5.09522472e-03, 8.41459714e-05, 2.35672254e-05,
|
||||
7.55872505e-05, 3.43949612e-06, 2.44153330e-05,
|
||||
8.28997024e-03, 7.64261509e-02]],
|
||||
|
||||
[[5.90021731e-04, 2.55342733e-05, 4.50698224e-05,
|
||||
5.30734135e-07, 1.80741761e-07, 1.11483792e-05,
|
||||
5.98539007e-06, 4.35015431e-04],
|
||||
[6.73107901e-03, 3.42109009e-04, 2.18579464e-03,
|
||||
1.13987259e-03, 1.03004157e-04, 1.14692946e-02,
|
||||
8.90976350e-02, 1.48149567e-01]]],
|
||||
|
||||
|
||||
[[[6.34648123e-02, 1.79187451e-02, 2.37462147e-04,
|
||||
3.55542558e-05, 7.63980455e-05, 2.90520820e-06,
|
||||
8.17644492e-06, 1.42930726e-03],
|
||||
[1.98699352e-02, 7.23695477e-03, 3.44076057e-04,
|
||||
2.15527721e-03, 1.13696383e-03, 7.87695658e-05,
|
||||
3.19047276e-03, 1.26774695e-02]],
|
||||
|
||||
[[8.81925054e-02, 8.33092133e-02, 2.51106301e-02,
|
||||
5.81007470e-04, 2.19065072e-03, 1.20221350e-03,
|
||||
7.56893839e-05, 2.76363377e-03],
|
||||
[8.03066603e-01, 8.90916999e-01, 9.72040418e-01,
|
||||
9.96011175e-01, 9.96489179e-01, 9.87210535e-01,
|
||||
8.99315113e-01, 7.51241236e-01]]]])
|
||||
|
||||
|
||||
class TestHamiltonAR2Short(MarkovAutoregression):
|
||||
# This is just a set of regression tests
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
true = {
|
||||
'params': np.r_[0.754673, 0.095915, -0.358811, 1.163516,
|
||||
np.exp(-0.262658)**2, 0.013486, -0.057521],
|
||||
'llf': -10.14066,
|
||||
'llf_fit': -4.0523073,
|
||||
'llf_fit_em': -8.885836
|
||||
}
|
||||
super().setup_class(
|
||||
true, rgnp[-10:], k_regimes=2, order=2, switching_ar=False)
|
||||
|
||||
def test_fit_em(self):
|
||||
with warnings.catch_warnings():
|
||||
warnings.simplefilter("ignore")
|
||||
super().test_fit_em()
|
||||
|
||||
def test_filter_output(self, **kwargs):
|
||||
res = self.result
|
||||
|
||||
# Filtered
|
||||
assert_allclose(res.filtered_joint_probabilities,
|
||||
hamilton_ar2_short_filtered_joint_probabilities)
|
||||
|
||||
# Predicted
|
||||
desired = hamilton_ar2_short_predicted_joint_probabilities
|
||||
if desired.ndim > res.predicted_joint_probabilities.ndim:
|
||||
desired = desired.sum(axis=-2)
|
||||
assert_allclose(res.predicted_joint_probabilities, desired)
|
||||
|
||||
def test_smoother_output(self, **kwargs):
|
||||
res = self.result
|
||||
|
||||
# Filtered
|
||||
assert_allclose(res.filtered_joint_probabilities,
|
||||
hamilton_ar2_short_filtered_joint_probabilities)
|
||||
|
||||
# Predicted
|
||||
desired = hamilton_ar2_short_predicted_joint_probabilities
|
||||
if desired.ndim > res.predicted_joint_probabilities.ndim:
|
||||
desired = desired.sum(axis=-2)
|
||||
assert_allclose(res.predicted_joint_probabilities, desired)
|
||||
|
||||
# Smoothed, entry-by-entry
|
||||
assert_allclose(
|
||||
res.smoothed_joint_probabilities[..., -1],
|
||||
hamilton_ar2_short_smoothed_joint_probabilities[..., -1])
|
||||
assert_allclose(
|
||||
res.smoothed_joint_probabilities[..., -2],
|
||||
hamilton_ar2_short_smoothed_joint_probabilities[..., -2])
|
||||
assert_allclose(
|
||||
res.smoothed_joint_probabilities[..., -3],
|
||||
hamilton_ar2_short_smoothed_joint_probabilities[..., -3])
|
||||
assert_allclose(
|
||||
res.smoothed_joint_probabilities[..., :-3],
|
||||
hamilton_ar2_short_smoothed_joint_probabilities[..., :-3])
|
||||
|
||||
|
||||
hamilton_ar4_filtered = [
|
||||
0.776712, 0.949192, 0.996320, 0.990258, 0.940111, 0.537442,
|
||||
0.140001, 0.008942, 0.048480, 0.614097, 0.910889, 0.995463,
|
||||
0.979465, 0.992324, 0.984561, 0.751038, 0.776268, 0.522048,
|
||||
0.814956, 0.821786, 0.472729, 0.673567, 0.029031, 0.001556,
|
||||
0.433276, 0.985463, 0.995025, 0.966067, 0.998445, 0.801467,
|
||||
0.960997, 0.996431, 0.461365, 0.199357, 0.027398, 0.703626,
|
||||
0.946388, 0.985321, 0.998244, 0.989567, 0.984510, 0.986811,
|
||||
0.793788, 0.973675, 0.984848, 0.990418, 0.918427, 0.998769,
|
||||
0.977647, 0.978742, 0.927635, 0.998691, 0.988934, 0.991654,
|
||||
0.999288, 0.999073, 0.918636, 0.987710, 0.966876, 0.910015,
|
||||
0.826150, 0.969451, 0.844049, 0.941525, 0.993363, 0.949978,
|
||||
0.615206, 0.970915, 0.787585, 0.707818, 0.200476, 0.050835,
|
||||
0.140723, 0.809850, 0.086422, 0.990344, 0.785963, 0.817425,
|
||||
0.659152, 0.996578, 0.992860, 0.948501, 0.996883, 0.999712,
|
||||
0.906694, 0.725013, 0.963690, 0.386960, 0.241302, 0.009078,
|
||||
0.015789, 0.000896, 0.541530, 0.928686, 0.953704, 0.992741,
|
||||
0.935877, 0.918958, 0.977316, 0.987941, 0.987300, 0.996769,
|
||||
0.645469, 0.921285, 0.999917, 0.949335, 0.968914, 0.886025,
|
||||
0.777141, 0.904381, 0.368277, 0.607429, 0.002491, 0.227610,
|
||||
0.871284, 0.987717, 0.288705, 0.512124, 0.030329, 0.005177,
|
||||
0.256183, 0.020955, 0.051620, 0.549009, 0.991715, 0.987892,
|
||||
0.995377, 0.999833, 0.993756, 0.956164, 0.927714]
|
||||
|
||||
hamilton_ar4_smoothed = [
|
||||
0.968096, 0.991071, 0.998559, 0.958534, 0.540652, 0.072784,
|
||||
0.010999, 0.006228, 0.172144, 0.898574, 0.989054, 0.998293,
|
||||
0.986434, 0.993248, 0.976868, 0.858521, 0.847452, 0.675670,
|
||||
0.596294, 0.165407, 0.035270, 0.127967, 0.007414, 0.004944,
|
||||
0.815829, 0.998128, 0.998091, 0.993227, 0.999283, 0.921100,
|
||||
0.977171, 0.971757, 0.124680, 0.063710, 0.114570, 0.954701,
|
||||
0.994852, 0.997302, 0.999345, 0.995817, 0.996218, 0.994580,
|
||||
0.933990, 0.996054, 0.998151, 0.996976, 0.971489, 0.999786,
|
||||
0.997362, 0.996755, 0.993053, 0.999947, 0.998469, 0.997987,
|
||||
0.999830, 0.999360, 0.953176, 0.992673, 0.975235, 0.938121,
|
||||
0.946784, 0.986897, 0.905792, 0.969755, 0.995379, 0.914480,
|
||||
0.772814, 0.931385, 0.541742, 0.394596, 0.063428, 0.027829,
|
||||
0.124527, 0.286105, 0.069362, 0.995950, 0.961153, 0.962449,
|
||||
0.945022, 0.999855, 0.998943, 0.980041, 0.999028, 0.999838,
|
||||
0.863305, 0.607421, 0.575983, 0.013300, 0.007562, 0.000635,
|
||||
0.001806, 0.002196, 0.803550, 0.972056, 0.984503, 0.998059,
|
||||
0.985211, 0.988486, 0.994452, 0.994498, 0.998873, 0.999192,
|
||||
0.870482, 0.976282, 0.999961, 0.984283, 0.973045, 0.786176,
|
||||
0.403673, 0.275418, 0.115199, 0.257560, 0.004735, 0.493936,
|
||||
0.907360, 0.873199, 0.052959, 0.076008, 0.001653, 0.000847,
|
||||
0.062027, 0.021257, 0.219547, 0.955654, 0.999851, 0.997685,
|
||||
0.998324, 0.999939, 0.996858, 0.969209, 0.927714]
|
||||
|
||||
|
||||
class TestHamiltonAR4(MarkovAutoregression):
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
# Results from E-views:
|
||||
# Dependent variable followed by a list of switching regressors:
|
||||
# rgnp c
|
||||
# List of non-switching regressors:
|
||||
# ar(1) ar(2) ar(3) ar(4)
|
||||
# Do not check "Regime specific error variances"
|
||||
# Switching type: Markov
|
||||
# Number of Regimes: 2
|
||||
# Probability regressors:
|
||||
# c
|
||||
# Method SWITCHREG
|
||||
# Sample 1951q1 1984q4
|
||||
true = {
|
||||
'params': np.r_[0.754673, 0.095915, -0.358811, 1.163516,
|
||||
np.exp(-0.262658)**2, 0.013486, -0.057521,
|
||||
-0.246983, -0.212923],
|
||||
'llf': -181.26339,
|
||||
'llf_fit': -181.26339,
|
||||
'llf_fit_em': -183.85444,
|
||||
'bse_oim': np.r_[.0965189, .0377362, .2645396, .0745187, np.nan,
|
||||
.1199942, .137663, .1069103, .1105311, ]
|
||||
}
|
||||
super().setup_class(
|
||||
true, rgnp, k_regimes=2, order=4, switching_ar=False)
|
||||
|
||||
def test_filtered_regimes(self):
|
||||
res = self.result
|
||||
assert_equal(len(res.filtered_marginal_probabilities[:, 1]),
|
||||
self.model.nobs)
|
||||
assert_allclose(res.filtered_marginal_probabilities[:, 1],
|
||||
hamilton_ar4_filtered, atol=1e-5)
|
||||
|
||||
def test_smoothed_regimes(self):
|
||||
res = self.result
|
||||
assert_equal(len(res.smoothed_marginal_probabilities[:, 1]),
|
||||
self.model.nobs)
|
||||
assert_allclose(res.smoothed_marginal_probabilities[:, 1],
|
||||
hamilton_ar4_smoothed, atol=1e-5)
|
||||
|
||||
def test_bse(self):
|
||||
# Cannot compare middle element of bse because we estimate sigma^2
|
||||
# rather than sigma
|
||||
bse = self.result.cov_params_approx.diagonal()**0.5
|
||||
assert_allclose(bse[:4], self.true['bse_oim'][:4], atol=1e-6)
|
||||
assert_allclose(bse[6:], self.true['bse_oim'][6:], atol=1e-6)
|
||||
|
||||
|
||||
class TestHamiltonAR2Switch(MarkovAutoregression):
|
||||
# Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
path = os.path.join(current_path, 'results',
|
||||
'results_predict_rgnp.csv')
|
||||
results = pd.read_csv(path)
|
||||
|
||||
true = {
|
||||
'params': np.r_[.3812383, .3564492, -.0055216, 1.195482,
|
||||
.6677098**2, .3710719, .4621503, .7002937,
|
||||
-.3206652],
|
||||
'llf': -179.32354,
|
||||
'llf_fit': -179.38684,
|
||||
'llf_fit_em': -184.99606,
|
||||
'bse_oim': np.r_[.1424841, .0994742, .2057086, .1225987, np.nan,
|
||||
.1754383, .1652473, .187409, .1295937],
|
||||
'smoothed0': results.iloc[3:]['switchar2_sm1'],
|
||||
'smoothed1': results.iloc[3:]['switchar2_sm2'],
|
||||
'predict0': results.iloc[3:]['switchar2_yhat1'],
|
||||
'predict1': results.iloc[3:]['switchar2_yhat2'],
|
||||
'predict_predicted': results.iloc[3:]['switchar2_pyhat'],
|
||||
'predict_filtered': results.iloc[3:]['switchar2_fyhat'],
|
||||
'predict_smoothed': results.iloc[3:]['switchar2_syhat'],
|
||||
}
|
||||
super().setup_class(
|
||||
true, rgnp, k_regimes=2, order=2)
|
||||
|
||||
def test_smoothed_marginal_probabilities(self):
|
||||
assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
|
||||
self.true['smoothed0'], atol=1e-6)
|
||||
assert_allclose(self.result.smoothed_marginal_probabilities[:, 1],
|
||||
self.true['smoothed1'], atol=1e-6)
|
||||
|
||||
def test_predict(self):
|
||||
# Smoothed
|
||||
actual = self.model.predict(
|
||||
self.true['params'], probabilities='smoothed')
|
||||
assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
|
||||
actual = self.model.predict(
|
||||
self.true['params'], probabilities=None)
|
||||
assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
|
||||
|
||||
actual = self.result.predict(probabilities='smoothed')
|
||||
assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
|
||||
actual = self.result.predict(probabilities=None)
|
||||
assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6)
|
||||
|
||||
def test_bse(self):
|
||||
# Cannot compare middle element of bse because we estimate sigma^2
|
||||
# rather than sigma
|
||||
bse = self.result.cov_params_approx.diagonal()**0.5
|
||||
assert_allclose(bse[:4], self.true['bse_oim'][:4], atol=1e-7)
|
||||
assert_allclose(bse[6:], self.true['bse_oim'][6:], atol=1e-7)
|
||||
|
||||
|
||||
hamilton_ar1_switch_filtered = [
|
||||
0.840288, 0.730337, 0.900234, 0.596492, 0.921618, 0.983828,
|
||||
0.959039, 0.898366, 0.477335, 0.251089, 0.049367, 0.386782,
|
||||
0.942868, 0.965632, 0.982857, 0.897603, 0.946986, 0.916413,
|
||||
0.640912, 0.849296, 0.778371, 0.954420, 0.929906, 0.723930,
|
||||
0.891196, 0.061163, 0.004806, 0.977369, 0.997871, 0.977950,
|
||||
0.896580, 0.963246, 0.430539, 0.906586, 0.974589, 0.514506,
|
||||
0.683457, 0.276571, 0.956475, 0.966993, 0.971618, 0.987019,
|
||||
0.916670, 0.921652, 0.930265, 0.655554, 0.965858, 0.964981,
|
||||
0.976790, 0.868267, 0.983240, 0.852052, 0.919150, 0.854467,
|
||||
0.987868, 0.935840, 0.958138, 0.979535, 0.956541, 0.716322,
|
||||
0.919035, 0.866437, 0.899609, 0.914667, 0.976448, 0.867252,
|
||||
0.953075, 0.977850, 0.884242, 0.688299, 0.968461, 0.737517,
|
||||
0.870674, 0.559413, 0.380339, 0.582813, 0.941311, 0.240020,
|
||||
0.999349, 0.619258, 0.828343, 0.729726, 0.991009, 0.966291,
|
||||
0.899148, 0.970798, 0.977684, 0.695877, 0.637555, 0.915824,
|
||||
0.434600, 0.771277, 0.113756, 0.144002, 0.008466, 0.994860,
|
||||
0.993173, 0.961722, 0.978555, 0.789225, 0.836283, 0.940383,
|
||||
0.968368, 0.974473, 0.980248, 0.518125, 0.904086, 0.993023,
|
||||
0.802936, 0.920906, 0.685445, 0.666524, 0.923285, 0.643861,
|
||||
0.938184, 0.008862, 0.945406, 0.990061, 0.991500, 0.486669,
|
||||
0.805039, 0.089036, 0.025067, 0.863309, 0.352784, 0.733295,
|
||||
0.928710, 0.984257, 0.926597, 0.959887, 0.984051, 0.872682,
|
||||
0.824375, 0.780157]
|
||||
|
||||
hamilton_ar1_switch_smoothed = [
|
||||
0.900074, 0.758232, 0.914068, 0.637248, 0.901951, 0.979905,
|
||||
0.958935, 0.888641, 0.261602, 0.148761, 0.056919, 0.424396,
|
||||
0.932184, 0.954962, 0.983958, 0.895595, 0.949519, 0.923473,
|
||||
0.678898, 0.848793, 0.807294, 0.958868, 0.942936, 0.809137,
|
||||
0.960892, 0.032947, 0.007127, 0.967967, 0.996551, 0.979278,
|
||||
0.896181, 0.987462, 0.498965, 0.908803, 0.986893, 0.488720,
|
||||
0.640492, 0.325552, 0.951996, 0.959703, 0.960914, 0.986989,
|
||||
0.916779, 0.924570, 0.935348, 0.677118, 0.960749, 0.958966,
|
||||
0.976974, 0.838045, 0.986562, 0.847774, 0.908866, 0.821110,
|
||||
0.984965, 0.915302, 0.938196, 0.976518, 0.973780, 0.744159,
|
||||
0.922006, 0.873292, 0.904035, 0.917547, 0.978559, 0.870915,
|
||||
0.948420, 0.979747, 0.884791, 0.711085, 0.973235, 0.726311,
|
||||
0.828305, 0.446642, 0.411135, 0.639357, 0.973151, 0.141707,
|
||||
0.999805, 0.618207, 0.783239, 0.672193, 0.987618, 0.964655,
|
||||
0.877390, 0.962437, 0.989002, 0.692689, 0.699370, 0.937934,
|
||||
0.522535, 0.824567, 0.058746, 0.146549, 0.009864, 0.994072,
|
||||
0.992084, 0.956945, 0.984297, 0.795926, 0.845698, 0.935364,
|
||||
0.963285, 0.972767, 0.992168, 0.528278, 0.826349, 0.996574,
|
||||
0.811431, 0.930873, 0.680756, 0.721072, 0.937977, 0.731879,
|
||||
0.996745, 0.016121, 0.951187, 0.989820, 0.996968, 0.592477,
|
||||
0.889144, 0.036015, 0.040084, 0.858128, 0.418984, 0.746265,
|
||||
0.907990, 0.980984, 0.900449, 0.934741, 0.986807, 0.872818,
|
||||
0.812080, 0.780157]
|
||||
|
||||
|
||||
class TestHamiltonAR1Switch(MarkovAutoregression):
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
# Results from E-views:
|
||||
# Dependent variable followed by a list of switching regressors:
|
||||
# rgnp c ar(1)
|
||||
# List of non-switching regressors: <blank>
|
||||
# Do not check "Regime specific error variances"
|
||||
# Switching type: Markov
|
||||
# Number of Regimes: 2
|
||||
# Probability regressors:
|
||||
# c
|
||||
# Method SWITCHREG
|
||||
# Sample 1951q1 1984q4
|
||||
true = {
|
||||
'params': np.r_[0.85472458, 0.53662099, 1.041419, -0.479157,
|
||||
np.exp(-0.231404)**2, 0.243128, 0.713029],
|
||||
'llf': -186.7575,
|
||||
'llf_fit': -186.7575,
|
||||
'llf_fit_em': -189.25446
|
||||
}
|
||||
super().setup_class(
|
||||
true, rgnp, k_regimes=2, order=1)
|
||||
|
||||
def test_filtered_regimes(self):
|
||||
assert_allclose(self.result.filtered_marginal_probabilities[:, 0],
|
||||
hamilton_ar1_switch_filtered, atol=1e-5)
|
||||
|
||||
def test_smoothed_regimes(self):
|
||||
assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
|
||||
hamilton_ar1_switch_smoothed, atol=1e-5)
|
||||
|
||||
def test_expected_durations(self):
|
||||
expected_durations = [6.883477, 1.863513]
|
||||
assert_allclose(self.result.expected_durations, expected_durations,
|
||||
atol=1e-5)
|
||||
|
||||
|
||||
hamilton_ar1_switch_tvtp_filtered = [
|
||||
0.999996, 0.999211, 0.999849, 0.996007, 0.999825, 0.999991,
|
||||
0.999981, 0.999819, 0.041745, 0.001116, 1.74e-05, 0.000155,
|
||||
0.999976, 0.999958, 0.999993, 0.999878, 0.999940, 0.999791,
|
||||
0.996553, 0.999486, 0.998485, 0.999894, 0.999765, 0.997657,
|
||||
0.999619, 0.002853, 1.09e-05, 0.999884, 0.999996, 0.999997,
|
||||
0.999919, 0.999987, 0.989762, 0.999807, 0.999978, 0.050734,
|
||||
0.010660, 0.000217, 0.006174, 0.999977, 0.999954, 0.999995,
|
||||
0.999934, 0.999867, 0.999824, 0.996783, 0.999941, 0.999948,
|
||||
0.999981, 0.999658, 0.999994, 0.999753, 0.999859, 0.999330,
|
||||
0.999993, 0.999956, 0.999970, 0.999996, 0.999991, 0.998674,
|
||||
0.999869, 0.999432, 0.999570, 0.999600, 0.999954, 0.999499,
|
||||
0.999906, 0.999978, 0.999712, 0.997441, 0.999948, 0.998379,
|
||||
0.999578, 0.994745, 0.045936, 0.006816, 0.027384, 0.000278,
|
||||
1.000000, 0.996382, 0.999541, 0.998130, 0.999992, 0.999990,
|
||||
0.999860, 0.999986, 0.999997, 0.998520, 0.997777, 0.999821,
|
||||
0.033353, 0.011629, 6.95e-05, 4.52e-05, 2.04e-06, 0.999963,
|
||||
0.999977, 0.999949, 0.999986, 0.999240, 0.999373, 0.999858,
|
||||
0.999946, 0.999972, 0.999991, 0.994039, 0.999817, 0.999999,
|
||||
0.999715, 0.999924, 0.997763, 0.997944, 0.999825, 0.996592,
|
||||
0.695147, 0.000161, 0.999665, 0.999928, 0.999988, 0.992742,
|
||||
0.374214, 0.001569, 2.16e-05, 0.000941, 4.32e-05, 0.000556,
|
||||
0.999955, 0.999993, 0.999942, 0.999973, 0.999999, 0.999919,
|
||||
0.999438, 0.998738]
|
||||
|
||||
hamilton_ar1_switch_tvtp_smoothed = [
|
||||
0.999997, 0.999246, 0.999918, 0.996118, 0.999740, 0.999990,
|
||||
0.999984, 0.999783, 0.035454, 0.000958, 1.53e-05, 0.000139,
|
||||
0.999973, 0.999939, 0.999994, 0.999870, 0.999948, 0.999884,
|
||||
0.997243, 0.999668, 0.998424, 0.999909, 0.999860, 0.998037,
|
||||
0.999559, 0.002533, 1.16e-05, 0.999801, 0.999993, 0.999997,
|
||||
0.999891, 0.999994, 0.990096, 0.999753, 0.999974, 0.048495,
|
||||
0.009289, 0.000542, 0.005991, 0.999974, 0.999929, 0.999995,
|
||||
0.999939, 0.999880, 0.999901, 0.996221, 0.999937, 0.999935,
|
||||
0.999985, 0.999450, 0.999995, 0.999768, 0.999897, 0.998930,
|
||||
0.999992, 0.999949, 0.999954, 0.999995, 0.999994, 0.998687,
|
||||
0.999902, 0.999547, 0.999653, 0.999538, 0.999966, 0.999485,
|
||||
0.999883, 0.999982, 0.999831, 0.996940, 0.999968, 0.998678,
|
||||
0.999780, 0.993895, 0.055372, 0.020421, 0.022913, 0.000127,
|
||||
1.000000, 0.997072, 0.999715, 0.996893, 0.999990, 0.999991,
|
||||
0.999811, 0.999978, 0.999998, 0.999100, 0.997866, 0.999787,
|
||||
0.034912, 0.009932, 5.91e-05, 3.99e-05, 1.77e-06, 0.999954,
|
||||
0.999976, 0.999932, 0.999991, 0.999429, 0.999393, 0.999845,
|
||||
0.999936, 0.999961, 0.999995, 0.994246, 0.999570, 1.000000,
|
||||
0.999702, 0.999955, 0.998611, 0.998019, 0.999902, 0.998486,
|
||||
0.673991, 0.000205, 0.999627, 0.999902, 0.999994, 0.993707,
|
||||
0.338707, 0.001359, 2.36e-05, 0.000792, 4.47e-05, 0.000565,
|
||||
0.999932, 0.999993, 0.999931, 0.999950, 0.999999, 0.999940,
|
||||
0.999626, 0.998738]
|
||||
|
||||
expected_durations = [
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391],
|
||||
[710.7573, 1.000391], [710.7573, 1.000391]]
|
||||
|
||||
|
||||
class TestHamiltonAR1SwitchTVTP(MarkovAutoregression):
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
# Results from E-views:
|
||||
# Dependent variable followed by a list of switching regressors:
|
||||
# rgnp c ar(1)
|
||||
# List of non-switching regressors: <blank>
|
||||
# Do not check "Regime specific error variances"
|
||||
# Switching type: Markov
|
||||
# Number of Regimes: 2
|
||||
# Probability regressors:
|
||||
# c recession
|
||||
# Method SWITCHREG
|
||||
# Sample 1951q1 1984q4
|
||||
true = {
|
||||
'params': np.r_[6.564923, 7.846371, -8.064123, -15.37636,
|
||||
1.027190, -0.719760,
|
||||
np.exp(-0.217003)**2, 0.161489, 0.022536],
|
||||
'llf': -163.914049,
|
||||
'llf_fit': -161.786477,
|
||||
'llf_fit_em': -163.914049
|
||||
}
|
||||
exog_tvtp = np.c_[np.ones(len(rgnp)), rec]
|
||||
super().setup_class(
|
||||
true, rgnp, k_regimes=2, order=1, exog_tvtp=exog_tvtp)
|
||||
|
||||
@pytest.mark.skip # TODO(ChadFulton): give reason for skip
|
||||
def test_fit_em(self):
|
||||
pass
|
||||
|
||||
def test_filtered_regimes(self):
|
||||
assert_allclose(self.result.filtered_marginal_probabilities[:, 0],
|
||||
hamilton_ar1_switch_tvtp_filtered, atol=1e-5)
|
||||
|
||||
def test_smoothed_regimes(self):
|
||||
assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
|
||||
hamilton_ar1_switch_tvtp_smoothed, atol=1e-5)
|
||||
|
||||
def test_expected_durations(self):
|
||||
assert_allclose(self.result.expected_durations, expected_durations,
|
||||
rtol=1e-5, atol=1e-7)
|
||||
|
||||
|
||||
class TestFilardo(MarkovAutoregression):
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
path = os.path.join(current_path, 'results', 'mar_filardo.csv')
|
||||
cls.mar_filardo = pd.read_csv(path)
|
||||
true = {
|
||||
'params': np.r_[4.35941747, -1.6493936, 1.7702123, 0.9945672,
|
||||
0.517298, -0.865888,
|
||||
np.exp(-0.362469)**2,
|
||||
0.189474, 0.079344, 0.110944, 0.122251],
|
||||
'llf': -586.5718,
|
||||
'llf_fit': -586.5718,
|
||||
'llf_fit_em': -586.5718
|
||||
}
|
||||
endog = cls.mar_filardo['dlip'].iloc[1:].values
|
||||
exog_tvtp = add_constant(
|
||||
cls.mar_filardo['dmdlleading'].iloc[:-1].values)
|
||||
super().setup_class(
|
||||
true, endog, k_regimes=2, order=4, switching_ar=False,
|
||||
exog_tvtp=exog_tvtp)
|
||||
|
||||
@pytest.mark.skip # TODO(ChadFulton): give reason for skip
|
||||
def test_fit(self, **kwargs):
|
||||
pass
|
||||
|
||||
@pytest.mark.skip # TODO(ChadFulton): give reason for skip
|
||||
def test_fit_em(self):
|
||||
pass
|
||||
|
||||
def test_filtered_regimes(self):
|
||||
assert_allclose(self.result.filtered_marginal_probabilities[:, 0],
|
||||
self.mar_filardo['filtered_0'].iloc[5:], atol=1e-5)
|
||||
|
||||
def test_smoothed_regimes(self):
|
||||
assert_allclose(self.result.smoothed_marginal_probabilities[:, 0],
|
||||
self.mar_filardo['smoothed_0'].iloc[5:], atol=1e-5)
|
||||
|
||||
def test_expected_durations(self):
|
||||
assert_allclose(self.result.expected_durations,
|
||||
self.mar_filardo[['duration0', 'duration1']].iloc[5:],
|
||||
rtol=1e-5, atol=1e-7)
|
||||
|
||||
|
||||
class TestFilardoPandas(MarkovAutoregression):
|
||||
@classmethod
|
||||
def setup_class(cls):
|
||||
path = os.path.join(current_path, 'results', 'mar_filardo.csv')
|
||||
cls.mar_filardo = pd.read_csv(path)
|
||||
cls.mar_filardo.index = pd.date_range('1948-02-01', '1991-04-01',
|
||||
freq='MS')
|
||||
true = {
|
||||
'params': np.r_[4.35941747, -1.6493936, 1.7702123, 0.9945672,
|
||||
0.517298, -0.865888,
|
||||
np.exp(-0.362469)**2,
|
||||
0.189474, 0.079344, 0.110944, 0.122251],
|
||||
'llf': -586.5718,
|
||||
'llf_fit': -586.5718,
|
||||
'llf_fit_em': -586.5718
|
||||
}
|
||||
endog = cls.mar_filardo['dlip'].iloc[1:]
|
||||
exog_tvtp = add_constant(
|
||||
cls.mar_filardo['dmdlleading'].iloc[:-1])
|
||||
super().setup_class(
|
||||
true, endog, k_regimes=2, order=4, switching_ar=False,
|
||||
exog_tvtp=exog_tvtp)
|
||||
|
||||
@pytest.mark.skip # TODO(ChadFulton): give reason for skip
|
||||
def test_fit(self, **kwargs):
|
||||
pass
|
||||
|
||||
@pytest.mark.skip # TODO(ChadFulton): give reason for skip
|
||||
def test_fit_em(self):
|
||||
pass
|
||||
|
||||
def test_filtered_regimes(self):
|
||||
assert_allclose(self.result.filtered_marginal_probabilities[0],
|
||||
self.mar_filardo['filtered_0'].iloc[5:], atol=1e-5)
|
||||
|
||||
def test_smoothed_regimes(self):
|
||||
assert_allclose(self.result.smoothed_marginal_probabilities[0],
|
||||
self.mar_filardo['smoothed_0'].iloc[5:], atol=1e-5)
|
||||
|
||||
def test_expected_durations(self):
|
||||
assert_allclose(self.result.expected_durations,
|
||||
self.mar_filardo[['duration0', 'duration1']].iloc[5:],
|
||||
rtol=1e-5, atol=1e-7)
|
||||
File diff suppressed because it is too large
Load Diff
@ -0,0 +1,317 @@
|
||||
"""
|
||||
General tests for Markov switching models
|
||||
|
||||
Author: Chad Fulton
|
||||
License: BSD-3
|
||||
"""
|
||||
|
||||
import numpy as np
|
||||
from numpy.testing import assert_equal, assert_allclose, assert_raises
|
||||
import pandas as pd
|
||||
|
||||
from statsmodels.tools.numdiff import approx_fprime_cs
|
||||
from statsmodels.tsa.regime_switching import markov_switching
|
||||
|
||||
|
||||
def test_params():
|
||||
def check_transtion_2(params):
|
||||
assert_equal(params['regime_transition'], np.s_[0:2])
|
||||
assert_equal(params[0, 'regime_transition'], [0])
|
||||
assert_equal(params[1, 'regime_transition'], [1])
|
||||
assert_equal(params['regime_transition', 0], [0])
|
||||
assert_equal(params['regime_transition', 1], [1])
|
||||
|
||||
def check_transition_3(params):
|
||||
assert_equal(params['regime_transition'], np.s_[0:6])
|
||||
assert_equal(params[0, 'regime_transition'], [0, 3])
|
||||
assert_equal(params[1, 'regime_transition'], [1, 4])
|
||||
assert_equal(params[2, 'regime_transition'], [2, 5])
|
||||
assert_equal(params['regime_transition', 0], [0, 3])
|
||||
assert_equal(params['regime_transition', 1], [1, 4])
|
||||
assert_equal(params['regime_transition', 2], [2, 5])
|
||||
|
||||
params = markov_switching.MarkovSwitchingParams(k_regimes=2)
|
||||
params['regime_transition'] = [1]
|
||||
assert_equal(params.k_params, 1 * 2)
|
||||
assert_equal(params[0], [0])
|
||||
assert_equal(params[1], [1])
|
||||
check_transtion_2(params)
|
||||
|
||||
params['exog'] = [0, 1]
|
||||
assert_equal(params.k_params, 1 * 2 + 1 + 1 * 2)
|
||||
assert_equal(params[0], [0, 2, 3])
|
||||
assert_equal(params[1], [1, 2, 4])
|
||||
check_transtion_2(params)
|
||||
assert_equal(params['exog'], np.s_[2:5])
|
||||
assert_equal(params[0, 'exog'], [2, 3])
|
||||
assert_equal(params[1, 'exog'], [2, 4])
|
||||
assert_equal(params['exog', 0], [2, 3])
|
||||
assert_equal(params['exog', 1], [2, 4])
|
||||
|
||||
params = markov_switching.MarkovSwitchingParams(k_regimes=3)
|
||||
params['regime_transition'] = [1, 1]
|
||||
assert_equal(params.k_params, 2 * 3)
|
||||
assert_equal(params[0], [0, 3])
|
||||
assert_equal(params[1], [1, 4])
|
||||
assert_equal(params[2], [2, 5])
|
||||
check_transition_3(params)
|
||||
|
||||
# Test for invalid parameter setting
|
||||
assert_raises(IndexError, params.__setitem__, None, [1, 1])
|
||||
|
||||
# Test for invalid parameter selection
|
||||
assert_raises(IndexError, params.__getitem__, None)
|
||||
assert_raises(IndexError, params.__getitem__, (0, 0))
|
||||
assert_raises(IndexError, params.__getitem__, ('exog', 'exog'))
|
||||
assert_raises(IndexError, params.__getitem__, ('exog', 0, 1))
|
||||
|
||||
|
||||
def test_init_endog():
|
||||
index = pd.date_range(start='1950-01-01', periods=10, freq='D')
|
||||
endog = [
|
||||
np.ones(10), pd.Series(np.ones(10), index=index), np.ones((10, 1)),
|
||||
pd.DataFrame(np.ones((10, 1)), index=index)
|
||||
]
|
||||
for _endog in endog:
|
||||
mod = markov_switching.MarkovSwitching(_endog, k_regimes=2)
|
||||
assert_equal(mod.nobs, 10)
|
||||
assert_equal(mod.endog, _endog.squeeze())
|
||||
assert_equal(mod.k_regimes, 2)
|
||||
assert_equal(mod.tvtp, False)
|
||||
assert_equal(mod.k_tvtp, 0)
|
||||
assert_equal(mod.k_params, 2)
|
||||
|
||||
# Invalid: k_regimes < 2
|
||||
endog = np.ones(10)
|
||||
assert_raises(ValueError, markov_switching.MarkovSwitching, endog,
|
||||
k_regimes=1)
|
||||
|
||||
# Invalid: multiple endog columns
|
||||
endog = np.ones((10, 2))
|
||||
assert_raises(ValueError, markov_switching.MarkovSwitching, endog,
|
||||
k_regimes=2)
|
||||
|
||||
|
||||
def test_init_exog_tvtp():
|
||||
endog = np.ones(10)
|
||||
exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]]
|
||||
mod = markov_switching.MarkovSwitching(endog, k_regimes=2,
|
||||
exog_tvtp=exog_tvtp)
|
||||
assert_equal(mod.tvtp, True)
|
||||
assert_equal(mod.k_tvtp, 2)
|
||||
|
||||
# Invalid exog_tvtp (too many obs)
|
||||
exog_tvtp = np.c_[np.ones((11, 1)), (np.arange(11) + 1)[:, np.newaxis]]
|
||||
assert_raises(ValueError, markov_switching.MarkovSwitching, endog,
|
||||
k_regimes=2, exog_tvtp=exog_tvtp)
|
||||
|
||||
|
||||
def test_transition_matrix():
|
||||
# k_regimes = 2
|
||||
endog = np.ones(10)
|
||||
mod = markov_switching.MarkovSwitching(endog, k_regimes=2)
|
||||
params = np.r_[0., 0., 1.]
|
||||
transition_matrix = np.zeros((2, 2, 1))
|
||||
transition_matrix[1, :] = 1.
|
||||
assert_allclose(mod.regime_transition_matrix(params), transition_matrix)
|
||||
|
||||
# k_regimes = 3
|
||||
endog = np.ones(10)
|
||||
mod = markov_switching.MarkovSwitching(endog, k_regimes=3)
|
||||
params = np.r_[[0]*3, [0.2]*3, 1.]
|
||||
transition_matrix = np.zeros((3, 3, 1))
|
||||
transition_matrix[1, :, 0] = 0.2
|
||||
transition_matrix[2, :, 0] = 0.8
|
||||
assert_allclose(mod.regime_transition_matrix(params), transition_matrix)
|
||||
|
||||
# k_regimes = 2, tvtp
|
||||
endog = np.ones(10)
|
||||
exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]]
|
||||
mod = markov_switching.MarkovSwitching(endog, k_regimes=2,
|
||||
exog_tvtp=exog_tvtp)
|
||||
|
||||
# If all TVTP regression coefficients are zero, then the logit transform
|
||||
# results in exp(0) / (1 + exp(0)) = 0.5 for all parameters; since it's
|
||||
# k_regimes=2 the remainder calculation is also 0.5.
|
||||
params = np.r_[0, 0, 0, 0]
|
||||
assert_allclose(mod.regime_transition_matrix(params), 0.5)
|
||||
|
||||
# Manually compute the TVTP coefficients
|
||||
params = np.r_[1, 2, 1, 2]
|
||||
transition_matrix = np.zeros((2, 2, 10))
|
||||
|
||||
coeffs0 = np.sum(exog_tvtp, axis=1)
|
||||
p11 = np.exp(coeffs0) / (1 + np.exp(coeffs0))
|
||||
transition_matrix[0, 0, :] = p11
|
||||
transition_matrix[1, 0, :] = 1 - p11
|
||||
|
||||
coeffs1 = np.sum(2 * exog_tvtp, axis=1)
|
||||
p21 = np.exp(coeffs1) / (1 + np.exp(coeffs1))
|
||||
transition_matrix[0, 1, :] = p21
|
||||
transition_matrix[1, 1, :] = 1 - p21
|
||||
assert_allclose(mod.regime_transition_matrix(params), transition_matrix,
|
||||
atol=1e-10)
|
||||
|
||||
# k_regimes = 3, tvtp
|
||||
endog = np.ones(10)
|
||||
exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]]
|
||||
mod = markov_switching.MarkovSwitching(
|
||||
endog, k_regimes=3, exog_tvtp=exog_tvtp)
|
||||
|
||||
# If all TVTP regression coefficients are zero, then the logit transform
|
||||
# results in exp(0) / (1 + exp(0) + exp(0)) = 1/3 for all parameters;
|
||||
# since it's k_regimes=3 the remainder calculation is also 1/3.
|
||||
params = np.r_[[0]*12]
|
||||
assert_allclose(mod.regime_transition_matrix(params), 1 / 3)
|
||||
|
||||
# Manually compute the TVTP coefficients for the first column
|
||||
params = np.r_[[0]*6, [2]*6]
|
||||
transition_matrix = np.zeros((3, 3, 10))
|
||||
|
||||
p11 = np.zeros(10)
|
||||
p12 = 2 * np.sum(exog_tvtp, axis=1)
|
||||
tmp = np.exp(np.c_[p11, p12]).T
|
||||
transition_matrix[:2, 0, :] = tmp / (1 + np.sum(tmp, axis=0))
|
||||
transition_matrix[2, 0, :] = (
|
||||
1 - np.sum(transition_matrix[:2, 0, :], axis=0))
|
||||
assert_allclose(mod.regime_transition_matrix(params)[:, 0, :],
|
||||
transition_matrix[:, 0, :], atol=1e-10)
|
||||
|
||||
|
||||
def test_initial_probabilities():
|
||||
endog = np.ones(10)
|
||||
mod = markov_switching.MarkovSwitching(endog, k_regimes=2)
|
||||
params = np.r_[0.5, 0.5, 1.]
|
||||
|
||||
# Valid known initial probabilities
|
||||
mod.initialize_known([0.2, 0.8])
|
||||
assert_allclose(mod.initial_probabilities(params), [0.2, 0.8])
|
||||
|
||||
# Invalid known initial probabilities (too many elements)
|
||||
assert_raises(ValueError, mod.initialize_known, [0.2, 0.2, 0.6])
|
||||
|
||||
# Invalid known initial probabilities (does not sum to 1)
|
||||
assert_raises(ValueError, mod.initialize_known, [0.2, 0.2])
|
||||
|
||||
# Valid steady-state probabilities
|
||||
mod.initialize_steady_state()
|
||||
assert_allclose(mod.initial_probabilities(params), [0.5, 0.5])
|
||||
|
||||
# Invalid steady-state probabilities (when mod has tvtp)
|
||||
endog = np.ones(10)
|
||||
mod = markov_switching.MarkovSwitching(endog, k_regimes=2, exog_tvtp=endog)
|
||||
assert_raises(ValueError, mod.initialize_steady_state)
|
||||
|
||||
|
||||
def test_logistic():
|
||||
logistic = markov_switching._logistic
|
||||
|
||||
# For a number, logistic(x) = np.exp(x) / (1 + np.exp(x))
|
||||
cases = [0, 10., -4]
|
||||
for x in cases:
|
||||
# Have to use allclose b/c logistic() actually uses logsumexp, so
|
||||
# they're not equal
|
||||
assert_allclose(logistic(x), np.exp(x) / (1 + np.exp(x)))
|
||||
|
||||
# For a vector, logistic(x) returns
|
||||
# np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) for each i
|
||||
# but squeezed
|
||||
cases = [[1.], [0, 1.], [-2, 3., 1.2, -30.]]
|
||||
for x in cases:
|
||||
actual = logistic(x)
|
||||
desired = [np.exp(i) / (1 + np.sum(np.exp(x))) for i in x]
|
||||
assert_allclose(actual, desired)
|
||||
|
||||
# For a 2-dim, logistic(x) returns
|
||||
# np.exp(x[i, t]) / (1 + np.sum(np.exp(x[:, t]))) for each i, each t
|
||||
# but squeezed
|
||||
case = [[1.]]
|
||||
actual = logistic(case)
|
||||
assert_equal(actual.shape, (1, 1))
|
||||
assert_allclose(actual, np.exp(1) / (1 + np.exp(1)))
|
||||
|
||||
# Here, np.array(case) is 2x1, so it is interpreted as i=0, 1 and t=0
|
||||
case = [[0], [1.]]
|
||||
actual = logistic(case)
|
||||
desired = [np.exp(i) / (1 + np.sum(np.exp(case))) for i in case]
|
||||
assert_allclose(actual, desired)
|
||||
|
||||
# Here, np.array(case) is 1x2, so it is interpreted as i=0 and t=0, 1
|
||||
case = [[0, 1.]]
|
||||
actual = logistic(case)
|
||||
desired = np.exp(case) / (1 + np.exp(case))
|
||||
assert_allclose(actual, desired)
|
||||
|
||||
# For a 3-dim, logistic(x) returns
|
||||
# np.exp(x[i, j, t]) / (1 + np.sum(np.exp(x[:, j, t])))
|
||||
# for each i, each j, each t
|
||||
case = np.arange(2*3*4).reshape(2, 3, 4)
|
||||
actual = logistic(case)
|
||||
for j in range(3):
|
||||
assert_allclose(actual[:, j, :], logistic(case[:, j, :]))
|
||||
|
||||
|
||||
def test_partials_logistic():
|
||||
# Here we compare to analytic derivatives and to finite-difference
|
||||
# approximations
|
||||
logistic = markov_switching._logistic
|
||||
partials_logistic = markov_switching._partials_logistic
|
||||
|
||||
# For a number, logistic(x) = np.exp(x) / (1 + np.exp(x))
|
||||
# Then d/dx = logistix(x) - logistic(x)**2
|
||||
cases = [0, 10., -4]
|
||||
for x in cases:
|
||||
assert_allclose(partials_logistic(x), logistic(x) - logistic(x)**2)
|
||||
assert_allclose(partials_logistic(x), approx_fprime_cs([x], logistic))
|
||||
|
||||
# For a vector, logistic(x) returns
|
||||
# np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) for each i
|
||||
# Then d logistic(x[i]) / dx[i] = (logistix(x) - logistic(x)**2)[i]
|
||||
# And d logistic(x[i]) / dx[j] = -(logistic(x[i]) * logistic[x[j]])
|
||||
cases = [[1.], [0, 1.], [-2, 3., 1.2, -30.]]
|
||||
for x in cases:
|
||||
evaluated = np.atleast_1d(logistic(x))
|
||||
partials = np.diag(evaluated - evaluated**2)
|
||||
for i in range(len(x)):
|
||||
for j in range(i):
|
||||
partials[i, j] = partials[j, i] = -evaluated[i] * evaluated[j]
|
||||
assert_allclose(partials_logistic(x), partials)
|
||||
assert_allclose(partials_logistic(x), approx_fprime_cs(x, logistic))
|
||||
|
||||
# For a 2-dim, logistic(x) returns
|
||||
# np.exp(x[i, t]) / (1 + np.sum(np.exp(x[:, t]))) for each i, each t
|
||||
# but squeezed
|
||||
case = [[1.]]
|
||||
evaluated = logistic(case)
|
||||
partial = [evaluated - evaluated**2]
|
||||
assert_allclose(partials_logistic(case), partial)
|
||||
assert_allclose(partials_logistic(case), approx_fprime_cs(case, logistic))
|
||||
|
||||
# # Here, np.array(case) is 2x1, so it is interpreted as i=0, 1 and t=0
|
||||
case = [[0], [1.]]
|
||||
evaluated = logistic(case)[:, 0]
|
||||
partials = np.diag(evaluated - evaluated**2)
|
||||
partials[0, 1] = partials[1, 0] = -np.multiply(*evaluated)
|
||||
assert_allclose(partials_logistic(case)[:, :, 0], partials)
|
||||
assert_allclose(partials_logistic(case),
|
||||
approx_fprime_cs(np.squeeze(case), logistic)[..., None])
|
||||
|
||||
# Here, np.array(case) is 1x2, so it is interpreted as i=0 and t=0, 1
|
||||
case = [[0, 1.]]
|
||||
evaluated = logistic(case)
|
||||
partials = (evaluated - evaluated**2)[None, ...]
|
||||
assert_allclose(partials_logistic(case), partials)
|
||||
assert_allclose(partials_logistic(case),
|
||||
approx_fprime_cs(case, logistic).T)
|
||||
|
||||
# For a 3-dim, logistic(x) returns
|
||||
# np.exp(x[i, j, t]) / (1 + np.sum(np.exp(x[:, j, t])))
|
||||
# for each i, each j, each t
|
||||
case = np.arange(2*3*4).reshape(2, 3, 4)
|
||||
evaluated = logistic(case)
|
||||
partials = partials_logistic(case)
|
||||
for t in range(4):
|
||||
for j in range(3):
|
||||
desired = np.diag(evaluated[:, j, t] - evaluated[:, j, t]**2)
|
||||
desired[0, 1] = desired[1, 0] = -np.multiply(*evaluated[:, j, t])
|
||||
assert_allclose(partials[..., j, t], desired)
|
||||
Reference in New Issue
Block a user