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, :, :]))
def test_predict():
# AR(1) without mean, k_regimes=2
endog = np.ones(10)
mod = markov_autoregression.MarkovAutoregression(endog,
k_regimes=2,
order=1,
trend='nc')
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 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
