def test_zeros_independent_of_ar(self):
q = 5
rng = default_rng(5)
b = rng.normal(size=q)
arma1 = Arma(rng.normal(size=3), b)
arma2 = Arma(rng.normal(size=5), b)
zeros1 = arma1.calculate_zeros()
zeros2 = arma2.calculate_zeros()
np.testing.assert_allclose(zeros1, zeros2)
def test_ma1(self):
b = [0.6]
ma1 = Arma([], b)
zeros = ma1.calculate_zeros()
self.assertEqual(len(zeros), 1)
self.assertAlmostEqual(zeros[0], -b[0])
def test_number_of_zeros_matches_ma_order(self):
q = 5
rng = default_rng(3)
ma = Arma([], rng.normal(size=q))
zeros = ma.calculate_zeros()
self.assertEqual(len(zeros), q)
def test_ma2(self):
b = [-0.5, -0.3]
ma2 = Arma([], b)
zeros = ma2.calculate_zeros()
self.assertEqual(len(zeros), 2)
zero_prod = np.prod(zeros)
zero_sum = np.sum(zeros)
np.testing.assert_allclose(zero_sum, -b[0], atol=1e-8)
np.testing.assert_allclose(zero_prod, b[1], atol=1e-8)
def test_product_of_monomials_based_on_zeros_recovers_ma_coeffs(self):
p = 4
q = 4
rng = default_rng(2)
arma = Arma(rng.normal(size=p), rng.normal(size=q))
zeros = arma.calculate_zeros()
coeffs = np.polynomial.polynomial.polyfromroots(zeros)
# 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.b)