def test_poles_independent_of_ma(self):
p = 5
rng = default_rng(5)
a = rng.normal(size=p)
arma1 = Arma(a, rng.normal(size=3))
arma2 = Arma(a, rng.normal(size=5))
poles1 = arma1.calculate_poles()
poles2 = arma2.calculate_poles()
np.testing.assert_allclose(poles1, poles2)
def test_ar1(self):
a = [0.7]
ar1 = Arma(a, [])
poles = ar1.calculate_poles()
self.assertEqual(len(poles), 1)
self.assertAlmostEqual(poles[0], a[0])
def test_number_of_poles_matches_ar_order(self):
p = 6
rng = default_rng(4)
ar = Arma(rng.normal(size=p), [])
poles = ar.calculate_poles()
self.assertEqual(len(poles), p)
def test_ar2(self):
a = [0.5, -0.7]
ar2 = Arma(a, [])
poles = ar2.calculate_poles()
self.assertEqual(len(poles), 2)
pole_prod = np.prod(poles)
pole_sum = np.sum(poles)
np.testing.assert_allclose(pole_sum, a[0], atol=1e-8)
np.testing.assert_allclose(pole_prod, -a[1], atol=1e-8)
def test_product_of_monomials_based_on_poles_recovers_ar_coeffs(self):
p = 5
q = 3
rng = default_rng(2)
arma = Arma(rng.normal(size=p), rng.normal(size=q))
poles = arma.calculate_poles()
coeffs = np.polynomial.polynomial.polyfromroots(poles)
# make sure the coefficients are real, up to tolerance
self.assertLess(np.max(np.abs(np.imag(coeffs))), 1e-6)
# ensure that the coefficients are ordered in the proper way
coeffs = np.flip(coeffs.real)
np.testing.assert_allclose(coeffs[1:], -arma.a)