def test_innovation_error(self):
model_ma = PureARMA(theta=[-0.9], sigma_sq=1)
self.assertAlmostEqual(model_ma.get_innovations_error(0), 1.81, 3)
self.assertAlmostEqual(model_ma.get_innovations_error(1), 1.362, 3)
self.assertAlmostEqual(model_ma.get_innovations_error(2), 1.215, 3)
self.assertAlmostEqual(model_ma.get_innovations_error(3), 1.144, 3)
self.assertAlmostEqual(model_ma.get_innovations_error(4), 1.102, 3)
self.assertAlmostEqual(model_ma.get_innovations_error(5), 1.075, 3)
def test_state_space_repr(self):
F = np.matrix([[0, 1], [0, 0]])
G = np.matrix([[0.5, 1]])
S = np.matrix([[0], [0]])
R = np.matrix([[0]])
Q = np.matrix([[0, 0], [0, 1]])
ma_model = PureARMA(theta=[0.5])
ma_statespace = ma_model.get_state_space_repr()
np.testing.assert_equal(ma_statespace.get_F(), F)
np.testing.assert_equal(ma_statespace.get_G(), G)
np.testing.assert_equal(ma_statespace.get_S(), S)
np.testing.assert_equal(ma_statespace.get_R(), R)
np.testing.assert_equal(ma_statespace.get_Q(), Q)
def test_innovation_r(self):
model_arma11 = PureARMA([0.2], [0.4], sigma_sq=5)
model_ma = PureARMA(theta=[0.5], sigma_sq=3)
model_arma23 = PureARMA(phi=[1, -0.24], theta=[0.4, 0.2, 0.1], sigma_sq=0.2)
self.assertAlmostEqual(model_arma11.get_r(0), 1.375, 4)
self.assertAlmostEqual(model_arma11.get_r(1), 1.0436, 4)
self.assertAlmostEqual(model_arma11.get_r(2), 1.0067, 4)
self.assertAlmostEqual(model_arma11.get_r(3), 1.0011, 4)
self.assertAlmostEqual(model_arma11.get_r(4), 1.0002, 4)
self.assertAlmostEqual(model_arma11.get_r(5), 1.0000, 4)
for n in range(6, 11):
self.assertAlmostEqual(model_arma11.get_r(n), 1, 5)
self.assertAlmostEqual(model_ma.get_r(0), (1 + 0.5 ** 2), 8)
self.assertAlmostEqual(model_arma23.get_r(0), 7.1713, 4)
self.assertAlmostEqual(model_arma23.get_r(1), 1.3856, 4)
self.assertAlmostEqual(model_arma23.get_r(2), 1.0057, 4)
def test_F(self):
ar_model = PureARMA(phi=[1, 2, 3], sigma_sq=2).get_state_space_repr()
ma_model = PureARMA(theta=[1, 2, 3], sigma_sq=3).get_state_space_repr()
arma_model = PureARMA(phi=[1, 2, 3], theta=[1, 2, 3], sigma_sq=4).get_state_space_repr()
noise_model = PureARMA(sigma_sq=5).get_state_space_repr()
ar_F = np.matrix([[0, 1, 0], [0, 0, 1], [3, 2, 1]])
ma_F = np.matrix([[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 0, 0, 0]])
arma_F = np.matrix([[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 3, 2, 1]])
noise_F = np.matrix([[0]])
np.testing.assert_equal(ar_model.get_F(), ar_F)
np.testing.assert_equal(ma_model.get_F(), ma_F)
np.testing.assert_equal(arma_model.get_F(), arma_F)
np.testing.assert_equal(noise_model.get_F(), noise_F)
def test_Q(self):
ar_model = PureARMA(phi=[1, 2, 3], sigma_sq=2).get_state_space_repr()
ma_model = PureARMA(theta=[1, 2, 3], sigma_sq=3).get_state_space_repr()
arma_model = PureARMA(phi=[1, 2, 3], theta=[1, 2, 3], sigma_sq=4).get_state_space_repr()
noise_model = PureARMA(sigma_sq=5).get_state_space_repr()
ar_Q = np.matrix([[0, 0, 0], [0, 0, 0], [0, 0, 2]])
ma_Q = np.matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3]])
arma_Q = np.matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 4]])
noise_Q = np.matrix([[5]])
np.testing.assert_equal(ar_model.get_Q(), ar_Q)
np.testing.assert_equal(ma_model.get_Q(), ma_Q)
np.testing.assert_equal(arma_model.get_Q(), arma_Q)
np.testing.assert_equal(noise_model.get_Q(), noise_Q)
def test_innovation_coefs(self):
model_arma11 = PureARMA([0.2], [0.4])
model_empty = PureARMA(sigma_sq=4)
model_arma23 = PureARMA(phi=[1, -0.24], theta=[0.4, 0.2, 0.1])
self.assertAlmostEqual(model_arma11.get_innovation_coef(1, 1), 0.2909, 4)
self.assertAlmostEqual(model_arma11.get_innovation_coef(2, 1), 0.3833, 4)
for n in range(6, 11):
self.assertAlmostEqual(model_arma11.get_innovation_coef(n, 1), 0.4, 4)
self.assertEqual(model_empty.get_innovation_coef(1, 1), 0)
self.assertEqual(model_empty.get_innovation_coef(9, 3), 0)
self.assertAlmostEqual(model_arma23.get_innovation_coef(1, 1), 0.8982, 4)
self.assertAlmostEqual(model_arma23.get_innovation_coef(2, 1), 1.3685, 4)
self.assertAlmostEqual(model_arma23.get_innovation_coef(2, 2), 0.7056, 4)
def test_parameters(self):
sigma_sq = 2
model = PureARMA([-1, 2, 3], [4, 5], sigma_sq)
self.assertEqual(model.get_phi(2), 2)
self.assertEqual(model.get_phi(0), 1)
self.assertEqual(model.get_phi(4), 0)
self.assertEqual(model.get_theta(2), 5)
self.assertEqual(model.get_theta(0), 1)
self.assertEqual(model.get_theta(3), 0)
self.assertEqual(model.get_sigma_sq(), sigma_sq)
def test_acf(self):
model_332 = PureARMA([1, -0.25], [1], 3)
model_ma = PureARMA([], [1, 2, 3])
model_empty = PureARMA()
model_arma23 = PureARMA(phi=[1, -0.24], theta=[0.4, 0.2, 0.1])
arma_model = PureARMA(phi=[0.7], theta=[0.3], sigma_sq=4)
for k in range(20):
self.assertAlmostEqual(model_332.auto_cov_funct(k), 3 * 2 ** -k * (32 / 3 + 8 * k))
for k in range(4, 100):
self.assertEqual(model_ma.auto_cov_funct(k), 0)
self.assertEqual(model_empty.auto_cov_funct(0), 1)
self.assertEqual(model_empty.auto_cov_funct(1), 0)
self.assertEqual(model_empty.auto_cov_funct(10), 0)
self.assertAlmostEqual(model_arma23.auto_cov_funct(0), 7.17133, 5)
self.assertAlmostEqual(model_arma23.auto_cov_funct(1), 6.44139, 5)
self.assertAlmostEqual(model_arma23.auto_cov_funct(2), 5.06027, 5)
self.assertAlmostEqual(arma_model.auto_cov_funct(0), 4 * (1 + 2 * 0.3 * 0.7 + 0.3 ** 2) / (1 - 0.7 ** 2), 6)
def test_ma_infty(self):
model_ma = PureARMA([], [1, 2, 3])
model_ar = PureARMA([0.5])
model_empty = PureARMA()
self.assertEqual(model_ma.get_ma_infty_coef(0), 1)
self.assertEqual(model_ma.get_ma_infty_coef(2), 2)
self.assertEqual(model_ma.get_ma_infty_coef(3), 3)
self.assertEqual(model_ma.get_ma_infty_coef(5), 0)
self.assertEqual(model_ma.get_ma_infty_coef(3), 3)
self.assertEqual(model_ar.get_ma_infty_coef(0), 1)
self.assertEqual(model_ar.get_ma_infty_coef(1), 0.5)
self.assertEqual(model_ar.get_ma_infty_coef(2), 0.25)
self.assertEqual(model_ar.get_ma_infty_coef(50), 0.5 ** 50)
self.assertEqual(model_empty.get_ma_infty_coef(0), 1)
self.assertEqual(model_empty.get_ma_infty_coef(1), 0)
self.assertEqual(model_empty.get_ma_infty_coef(10), 0)
def test_kappa_w(self):
theta = 0.4
sigma_sq = 3
ma_model = PureARMA(theta=[theta], sigma_sq=sigma_sq)
arma_model = PureARMA(phi=[0.7], theta=[0.3], sigma_sq=4)
model_arma23 = PureARMA(phi=[1, -0.24], theta=[0.4, 0.2, 0.1])
self.assertAlmostEqual(ma_model._kappa_w(1, 1), 1 + theta ** 2)
self.assertAlmostEqual(ma_model._kappa_w(2, 2), 1 + theta ** 2)
self.assertAlmostEqual(ma_model._kappa_w(3, 3), 1 + theta ** 2)
self.assertAlmostEqual(ma_model._kappa_w(1, 3), 0)
self.assertAlmostEqual(ma_model._kappa_w(1, 2), theta)
self.assertAlmostEqual(arma_model._kappa_w(1, 1), (1 + 2 * 0.3 * 0.7 + 0.3 ** 2) / (1 - 0.7 ** 2))
self.assertAlmostEqual(arma_model._kappa_w(2, 2), 1 + 0.3 ** 2)
self.assertAlmostEqual(arma_model._kappa_w(3, 3), 1 + 0.3 ** 2)
self.assertAlmostEqual(arma_model._kappa_w(1, 3), 0)
self.assertAlmostEqual(arma_model._kappa_w(1, 4), 0)
self.assertAlmostEqual(arma_model._kappa_w(1, 5), 0)
self.assertAlmostEqual(arma_model._kappa_w(20, 30), 0)
self.assertAlmostEqual(arma_model._kappa_w(1, 2), 0.3)
self.assertAlmostEqual(arma_model._kappa_w(3, 2), 0.3)
self.assertAlmostEqual(arma_model._kappa_w(16, 15), 0.3)
self.assertAlmostEqual(model_arma23._kappa_w(1, 1), 7.17133, 5)
self.assertAlmostEqual(model_arma23._kappa_w(1, 2), 6.44139, 5)
self.assertAlmostEqual(model_arma23._kappa_w(1, 3), 5.06027, 5)
self.assertAlmostEqual(model_arma23._kappa_w(4, 7), 0.1, 5)
self.assertAlmostEqual(model_arma23._kappa_w(1, 5), 0, 5)
self.assertAlmostEqual(model_arma23._kappa_w(2, 2), 7.17133, 5)