def generate_data(self, cc=((1, 0), (0, 1))):
var = VAR(2)
var.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
l = (1000, 100)
x = var.simulate(l, lambda: np.random.randn(2).dot(cc))
self.assertEqual(x.shape, (l[1], 2, l[0]))
return x, var
def test_whiteness(self):
np.random.seed(91)
var = VARBase(0)
var.residuals = np.random.randn(10, 5, 100)
pr = sp.plot_whiteness(var, 20, repeats=100)
self.assertGreater(pr, 0.05)
def test_whiteness(self):
np.random.seed(91)
var = VARBase(0)
var.residuals = np.random.randn(10, 5, 100)
pr = sp.plot_whiteness(var, 20, repeats=100)
self.assertGreater(pr, 0.05)
def test_stable(self):
var = VAR(1)
# Stable AR model -- rule of thumb: sum(coefs) < 1
var.coef = np.asarray([[0.5, 0.3]])
self.assertTrue(var.is_stable())
# Unstable AR model -- rule of thumb: sum(coefs) > 1
var.coef = np.asarray([[0.5, 0.7]])
self.assertFalse(var.is_stable())
def test_yulewalker(self):
np.random.seed(7353)
x, var0 = self.generate_data([[1, 2], [3, 4]])
acms = [acm(x, l) for l in range(var0.p+1)]
var = VAR(var0.p)
var.from_yw(acms)
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.all(np.abs(var0.coef - var.coef) < 0.02))
self.assertTrue(np.all(np.abs(var0.rescov - var.rescov) < 0.02))
def test_yulewalker(self):
np.random.seed(7353)
x, var0 = self.generate_data([[1, 2], [3, 4]])
acms = [acm(x, l) for l in range(var0.p + 1)]
var = VAR(var0.p)
var.from_yw(acms)
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.all(np.abs(var0.coef - var.coef) < 0.02))
self.assertTrue(np.all(np.abs(var0.rescov - var.rescov) < 0.02))
def test_whiteness(self):
np.random.seed(91)
r = np.random.randn(80, 15, 100) # gaussian white noise
r0 = r.copy()
var = VAR(0, n_jobs=-1)
var.residuals = r
p = var.test_whiteness(20, random_state=1)
self.assertTrue(np.all(r == r0)) # make sure we don't modify the input
self.assertGreater(p, 0.01) # test should be non-significant for white noise
r[:, 1, 3:] = r[:, 0, :-3] # create cross-correlation at lag 3
p = var.test_whiteness(20)
self.assertLessEqual(p, 0.01) # now test should be significant
def test_simulate(self):
noisefunc = lambda: [1, 1] # use deterministic function instead of noise
num_samples = 100
b = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
var = VAR(2)
var.coef = b
np.random.seed(42)
x = var.simulate(num_samples, noisefunc)
# make sure we got expected values within reasonable accuracy
for n in range(10, num_samples):
self.assertTrue(np.all(
np.abs(x[n, :] - 1 - np.dot(b[:, 0::2], x[n - 1, :]) - np.dot(b[:, 1::2], x[n - 2, :])) < 1e-10))
def test_whiteness(self):
np.random.seed(91)
r = np.random.randn(100, 5, 10) # gaussian white noise
r0 = r.copy()
var = VAR(0)
var.residuals = r
p = var.test_whiteness(20)
self.assertTrue(np.all(r == r0)) # make sure we don't modify the input
self.assertGreater(
p, 0.01) # test should be non-significant for white noise
r[3:, 1, :] = r[:-3, 0, :] # create cross-correlation at lag 3
p = var.test_whiteness(20)
self.assertLessEqual(p, 0.01) # now test should be significant
def test_simulate(self):
noisefunc = lambda: [1, 1
] # use deterministic function instead of noise
num_samples = 100
b = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
var = VAR(2)
var.coef = b
np.random.seed(42)
x = var.simulate(num_samples, noisefunc)
# make sure we got expected values within reasonable accuracy
for n in range(10, num_samples):
self.assertTrue(
np.all(
np.abs(x[n, :] - 1 - np.dot(b[:, 0::2], x[n - 1, :]) -
np.dot(b[:, 1::2], x[n - 2, :])) < 1e-10))
def generate_data(self, cc=((1, 0), (0, 1))):
var = VAR(2)
var.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
l = (1000, 100)
x = var.simulate(l, lambda: np.random.randn(2).dot(cc))
return x, var