def test_egarch_100(self):
egarch = EGARCH(p=1, o=0, q=0)
sv = egarch.starting_values(self.resids)
assert_equal(sv.shape[0], egarch.num_params)
backcast = egarch.backcast(self.resids)
w = 0.94 ** np.arange(75)
backcast_test = np.sum((self.resids[:75] ** 2) * (w / w.sum()))
assert_almost_equal(backcast, np.log(backcast_test))
var_bounds = egarch.variance_bounds(self.resids)
parameters = np.array([.1, .4])
egarch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
lnsigma2 = np.empty(self.T)
std_resids = np.empty(self.T)
abs_std_resids = np.empty(self.T)
rec.egarch_recursion(parameters, self.resids, cond_var_direct, 1, 0, 0,
self.T, backcast, var_bounds, lnsigma2,
std_resids, abs_std_resids)
assert_allclose(self.sigma2, cond_var_direct)
state = self.rng.get_state()
rng = Normal()
rng.random_state.set_state(state)
sim_data = egarch.simulate(parameters, self.T, rng.simulate([]))
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + 500)
initial_value = 0.1 / (1 - 0.95)
lnsigma2 = np.zeros(self.T + 500)
lnsigma2[0] = initial_value
sigma2 = np.zeros(self.T + 500)
sigma2[0] = np.exp(lnsigma2[0])
data = np.zeros(self.T + 500)
data[0] = np.sqrt(sigma2[0]) * e[0]
norm_const = np.sqrt(2 / np.pi)
for t in range(1, self.T + 500):
lnsigma2[t] = parameters[0]
lnsigma2[t] += parameters[1] * (np.abs(e[t - 1]) - norm_const)
sigma2 = np.exp(lnsigma2)
data = e * np.sqrt(sigma2)
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))
def test_egarch_100(self):
egarch = EGARCH(p=1, o=0, q=0)
sv = egarch.starting_values(self.resids)
assert_equal(sv.shape[0], egarch.num_params)
backcast = egarch.backcast(self.resids)
w = 0.94 ** np.arange(75)
backcast_test = np.sum((self.resids[:75] ** 2) * (w / w.sum()))
assert_almost_equal(backcast, np.log(backcast_test))
var_bounds = egarch.variance_bounds(self.resids)
parameters = np.array([.1, .4])
egarch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
lnsigma2 = np.empty(self.T)
std_resids = np.empty(self.T)
abs_std_resids = np.empty(self.T)
rec.egarch_recursion(parameters, self.resids, cond_var_direct, 1, 0, 0,
self.T, backcast, var_bounds, lnsigma2,
std_resids, abs_std_resids)
assert_allclose(self.sigma2, cond_var_direct)
state = np.random.get_state()
rng = Normal()
sim_data = egarch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
initial_value = 0.1 / (1 - 0.95)
lnsigma2 = np.zeros(self.T + 500)
lnsigma2[0] = initial_value
sigma2 = np.zeros(self.T + 500)
sigma2[0] = np.exp(lnsigma2[0])
data = np.zeros(self.T + 500)
data[0] = np.sqrt(sigma2[0]) * e[0]
norm_const = np.sqrt(2 / np.pi)
for t in range(1, self.T + 500):
lnsigma2[t] = parameters[0]
lnsigma2[t] += parameters[1] * (np.abs(e[t - 1]) - norm_const)
sigma2 = np.exp(lnsigma2)
data = e * np.sqrt(sigma2)
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))
def test_egarch(self):
egarch = EGARCH(p=1, o=1, q=1)
sv = egarch.starting_values(self.resids)
assert_equal(sv.shape[0], egarch.num_params)
bounds = egarch.bounds(self.resids)
assert_equal(len(bounds), egarch.num_params)
const = np.log(10000.0)
lnv = np.log(np.mean(self.resids ** 2.0))
assert_equal(bounds[0], (lnv - const, lnv + const))
assert_equal(bounds[1], (-np.inf, np.inf))
assert_equal(bounds[2], (-np.inf, np.inf))
assert_equal(bounds[3], (0.0, 1.0))
backcast = egarch.backcast(self.resids)
w = 0.94 ** np.arange(75)
backcast_test = np.sum((self.resids[:75] ** 2) * (w / w.sum()))
assert_almost_equal(backcast, np.log(backcast_test))
var_bounds = egarch.variance_bounds(self.resids)
parameters = np.array([.1, .1, -.1, .95])
egarch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
lnsigma2 = np.empty(self.T)
std_resids = np.empty(self.T)
abs_std_resids = np.empty(self.T)
rec.egarch_recursion(parameters, self.resids, cond_var_direct, 1, 1, 1,
self.T, backcast, var_bounds, lnsigma2,
std_resids, abs_std_resids)
assert_allclose(self.sigma2, cond_var_direct)
a, b = egarch.constraints()
a_target = np.vstack((np.array([[0, 0, 0, -1.0]])))
b_target = np.array([-1.0])
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
state = np.random.get_state()
rng = Normal()
sim_data = egarch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
initial_value = 0.1 / (1 - 0.95)
lnsigma2 = np.zeros(self.T + 500)
lnsigma2[0] = initial_value
sigma2 = np.zeros(self.T + 500)
sigma2[0] = np.exp(lnsigma2[0])
data = np.zeros(self.T + 500)
data[0] = np.sqrt(sigma2[0]) * e[0]
norm_const = np.sqrt(2 / np.pi)
for t in range(1, self.T + 500):
lnsigma2[t] = parameters[0]
lnsigma2[t] += parameters[1] * (np.abs(e[t - 1]) - norm_const)
lnsigma2[t] += parameters[2] * e[t - 1]
lnsigma2[t] += parameters[3] * lnsigma2[t - 1]
sigma2 = np.exp(lnsigma2)
data = e * np.sqrt(sigma2)
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 = egarch.parameter_names()
names_target = ['omega', 'alpha[1]', 'gamma[1]', 'beta[1]']
assert_equal(names, names_target)
assert_equal(egarch.name, 'EGARCH')
assert_equal(egarch.num_params, 4)
assert_equal(egarch.p, 1)
assert_equal(egarch.o, 1)
assert_equal(egarch.q, 1)
assert isinstance(egarch.__str__(), str)
txt = egarch.__repr__()
assert str(hex(id(egarch))) in txt
with pytest.raises(ValueError):
EGARCH(p=0, o=0, q=1)
with pytest.raises(ValueError):
EGARCH(p=1, o=1, q=-1)
def test_egarch(self):
egarch = EGARCH(p=1, o=1, q=1)
sv = egarch.starting_values(self.resids)
assert_equal(sv.shape[0], egarch.num_params)
bounds = egarch.bounds(self.resids)
assert_equal(len(bounds), egarch.num_params)
const = np.log(10000.0)
lnv = np.log(np.mean(self.resids ** 2.0))
assert_equal(bounds[0], (lnv - const, lnv + const))
assert_equal(bounds[1], (-np.inf, np.inf))
assert_equal(bounds[2], (-np.inf, np.inf))
assert_equal(bounds[3], (0.0, 1.0))
backcast = egarch.backcast(self.resids)
w = 0.94 ** np.arange(75)
backcast_test = np.sum((self.resids[:75] ** 2) * (w / w.sum()))
assert_almost_equal(backcast, np.log(backcast_test))
var_bounds = egarch.variance_bounds(self.resids)
parameters = np.array([.1, .1, -.1, .95])
egarch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
lnsigma2 = np.empty(self.T)
std_resids = np.empty(self.T)
abs_std_resids = np.empty(self.T)
rec.egarch_recursion(parameters, self.resids, cond_var_direct, 1, 1, 1,
self.T, backcast, var_bounds, lnsigma2, std_resids,
abs_std_resids)
assert_allclose(self.sigma2, cond_var_direct)
A, b = egarch.constraints()
A_target = np.vstack((np.array([[0, 0, 0, -1.0]])))
b_target = np.array([-1.0])
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
state = np.random.get_state()
rng = Normal()
sim_data = egarch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
initial_value = 0.1 / (1 - 0.95)
lnsigma2 = np.zeros(self.T + 500)
lnsigma2[0] = initial_value
sigma2 = np.zeros(self.T + 500)
sigma2[0] = np.exp(lnsigma2[0])
data = np.zeros(self.T + 500)
data[0] = np.sqrt(sigma2[0]) * e[0]
norm_const = np.sqrt(2 / np.pi)
for t in range(1, self.T + 500):
lnsigma2[t] = parameters[0]
lnsigma2[t] += parameters[1] * (np.abs(e[t - 1]) - norm_const)
lnsigma2[t] += parameters[2] * e[t - 1]
lnsigma2[t] += parameters[3] * lnsigma2[t - 1]
sigma2 = np.exp(lnsigma2)
data = e * np.sqrt(sigma2)
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 = egarch.parameter_names()
names_target = ['omega', 'alpha[1]', 'gamma[1]', 'beta[1]']
assert_equal(names, names_target)
assert_equal(egarch.name, 'EGARCH')
assert_equal(egarch.num_params, 4)
assert_equal(egarch.p, 1)
assert_equal(egarch.o, 1)
assert_equal(egarch.q, 1)