def test_arch(self):
arch = ARCH()
sv = arch.starting_values(self.resids)
assert_equal(sv.shape[0], arch.num_params)
bounds = arch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(self.resids ** 2.0)))
assert_equal(bounds[1], (0.0, 1.0))
backcast = arch.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
parameters = np.array([0.5, 0.7])
var_bounds = arch.variance_bounds(self.resids)
arch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.arch_recursion(parameters, self.resids, cond_var_direct, 1,
self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
a, b = arch.constraints()
a_target = np.vstack((np.eye(2), np.array([[0, -1.0]])))
b_target = np.array([0.0, 0.0, -1.0])
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
state = self.rng.get_state()
rng = Normal()
rng.random_state.set_state(state)
sim_data = arch.simulate(parameters, self.T, rng.simulate([]))
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + 500)
initial_value = 1.0
sigma2 = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
for t in range(self.T + 500):
sigma2[t] = parameters[0]
shock = initial_value if t == 0 else data[t - 1] ** 2.0
sigma2[t] += parameters[1] * shock
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data - sim_data[0] + 1.0, np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = arch.parameter_names()
names_target = ['omega', 'alpha[1]']
assert_equal(names, names_target)
assert_equal(arch.name, 'ARCH')
assert_equal(arch.num_params, 2)
assert_equal(arch.p, 1)
assert isinstance(arch.__str__(), str)
txt = arch.__repr__()
assert str(hex(id(arch))) in txt
def test_arch(self):
arch = ARCH()
sv = arch.starting_values(self.resids)
assert_equal(sv.shape[0], arch.num_params)
bounds = arch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(self.resids ** 2.0)))
assert_equal(bounds[1], (0.0, 1.0))
backcast = arch.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
parameters = np.array([0.5, 0.7])
var_bounds = arch.variance_bounds(self.resids)
arch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.arch_recursion(parameters, self.resids, cond_var_direct, 1,
self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
A, b = arch.constraints()
A_target = np.vstack((np.eye(2), np.array([[0, -1.0]])))
b_target = np.array([0.0, 0.0, -1.0])
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
state = np.random.get_state()
rng = Normal()
sim_data = arch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
initial_value = 1.0
sigma2 = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
for t in range(self.T + 500):
sigma2[t] = parameters[0]
shock = initial_value if t == 0 else data[t - 1] ** 2.0
sigma2[t] += parameters[1] * shock
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data - sim_data[0] + 1.0, np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = arch.parameter_names()
names_target = ['omega', 'alpha[1]']
assert_equal(names, names_target)
assert_equal(arch.name, 'ARCH')
assert_equal(arch.num_params, 2)
assert_equal(arch.p, 1)
assert_true(isinstance(arch.__str__(), str))
repr = arch.__repr__()
assert_true(str(hex(id(arch))) in repr)
def test_arch_multiple_lags(self):
arch = ARCH(p=5)
sv = arch.starting_values(self.resids)
assert_equal(sv.shape[0], arch.num_params)
bounds = arch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(self.resids ** 2.0)))
for i in range(1, 6):
assert_equal(bounds[i], (0.0, 1.0))
var_bounds = arch.variance_bounds(self.resids)
backcast = arch.backcast(self.resids)
parameters = np.array([0.25, 0.17, 0.16, 0.15, 0.14, 0.13])
arch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.arch_recursion(parameters, self.resids, cond_var_direct, 5,
self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
a, b = arch.constraints()
a_target = np.vstack((np.eye(6),
np.array([[0, -1.0, -1.0, -1.0, -1.0, -1.0]])))
b_target = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0])
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
state = self.rng.get_state()
rng = Normal()
rng.random_state.set_state(state)
sim_data = arch.simulate(parameters, self.T, rng.simulate([]))
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + 500)
initial_value = 1.0
sigma2 = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
for t in range(self.T + 500):
sigma2[t] = parameters[0]
for i in range(5):
if t - i - 1 < 0:
sigma2[t] += parameters[i + 1] * initial_value
else:
sigma2[t] += parameters[i + 1] * data[t - i - 1] ** 2.0
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data - sim_data[0] + 1.0, np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = arch.parameter_names()
names_target = ['omega']
names_target.extend(['alpha[' + str(i + 1) + ']' for i in range(5)])
assert_equal(names, names_target)
assert_equal(arch.num_params, 6)
assert_equal(arch.name, 'ARCH')
def test_arch_multiple_lags(self):
arch = ARCH(p=5)
sv = arch.starting_values(self.resids)
assert_equal(sv.shape[0], arch.num_params)
bounds = arch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(self.resids ** 2.0)))
for i in range(1, 6):
assert_equal(bounds[i], (0.0, 1.0))
var_bounds = arch.variance_bounds(self.resids)
backcast = arch.backcast(self.resids)
parameters = np.array([0.25, 0.17, 0.16, 0.15, 0.14, 0.13])
arch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.arch_recursion(parameters, self.resids, cond_var_direct, 5,
self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
A, b = arch.constraints()
A_target = np.vstack((np.eye(6),
np.array([[0, -1.0, -1.0, -1.0, -1.0, -1.0]])))
b_target = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0])
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
state = np.random.get_state()
rng = Normal()
sim_data = arch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
initial_value = 1.0
sigma2 = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
for t in range(self.T + 500):
sigma2[t] = parameters[0]
for i in range(5):
if t - i - 1 < 0:
sigma2[t] += parameters[i + 1] * initial_value
else:
sigma2[t] += parameters[i + 1] * data[t - i - 1] ** 2.0
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data - sim_data[0] + 1.0, np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = arch.parameter_names()
names_target = ['omega']
names_target.extend(['alpha[' + str(i + 1) + ']' for i in range(5)])
assert_equal(names, names_target)
assert_equal(arch.num_params, 6)
assert_equal(arch.name, 'ARCH')
