def test_ewma(self):
ewma = EWMAVariance()
sv = ewma.starting_values(self.resids)
assert_equal(sv.shape[0], ewma.num_params)
bounds = ewma.bounds(self.resids)
assert_equal(len(bounds), 0)
var_bounds = ewma.variance_bounds(self.resids)
backcast = ewma.backcast(self.resids)
parameters = np.array([])
names = ewma.parameter_names()
names_target = []
assert_equal(names, names_target)
ewma.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
parameters = np.array([0.0, 0.06, 0.94])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
# sigma3 = np.zeros_like(self.sigma2)
# sigma3[0] = backcast
# for t in range(1,self.T):
# sigma3[t] = 0.94 * sigma3[t-1] + 0.06 * self.resids[t-1]**2.0
assert_allclose(self.sigma2 / cond_var_direct,
np.ones_like(self.sigma2))
A, b = ewma.constraints()
A_target = np.empty((0, 0))
b_target = np.empty((0,))
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
state = np.random.get_state()
rng = Normal()
sim_data = ewma.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)
sigma2[0] = initial_value
data[0] = np.sqrt(initial_value)
for t in range(1, self.T + 500):
sigma2[t] = 0.94 * sigma2[t - 1] + 0.06 * data[t - 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))
assert_equal(ewma.num_params, 0)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
def test_ewma(self):
ewma = EWMAVariance()
sv = ewma.starting_values(self.resids)
assert_equal(sv.shape[0], ewma.num_params)
bounds = ewma.bounds(self.resids)
assert_equal(len(bounds), 0)
var_bounds = ewma.variance_bounds(self.resids)
backcast = ewma.backcast(self.resids)
parameters = np.array([])
names = ewma.parameter_names()
names_target = []
assert_equal(names, names_target)
ewma.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
parameters = np.array([0.0, 0.06, 0.94])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2 / cond_var_direct,
np.ones_like(self.sigma2))
a, b = ewma.constraints()
a_target = np.empty((0, 0))
b_target = np.empty((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 = ewma.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)
sigma2[0] = initial_value
data[0] = np.sqrt(initial_value)
for t in range(1, self.T + 500):
sigma2[t] = 0.94 * sigma2[t - 1] + 0.06 * data[t - 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))
assert_equal(ewma.num_params, 0)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
def test_garch_no_symmetric(self):
garch = GARCH(p=0, o=1, q=1)
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(self.resids ** 2.0)))
assert_equal(bounds[1], (0.0, 2.0))
assert_equal(bounds[2], (0.0, 1.0))
var_bounds = garch.variance_bounds(self.resids)
backcast = garch.backcast(self.resids)
parameters = np.array([.1, .1, .8])
names = garch.parameter_names()
names_target = ['omega', 'gamma[1]', 'beta[1]']
assert_equal(names, names_target)
garch.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
0, 1, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
a, b = garch.constraints()
a_target = np.vstack((np.eye(3), np.array([[0, -0.5, -1.0]])))
b_target = np.array([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 = garch.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 = 0.5 * initial_value if t == 0 else \
data[t - 1] ** 2.0 * (data[t - 1] < 0)
sigma2[t] += parameters[1] * shock
lagged_value = initial_value if t == 0 else sigma2[t - 1]
sigma2[t] += parameters[2] * lagged_value
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))
assert_equal(garch.p, 0)
assert_equal(garch.o, 1)
assert_equal(garch.q, 1)
assert_equal(garch.num_params, 3)
assert_equal(garch.name, 'GJR-GARCH')
def test_garch_no_symmetric(self):
garch = GARCH(p=0, o=1, q=1)
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(self.resids ** 2.0)))
assert_equal(bounds[1], (0.0, 2.0))
assert_equal(bounds[2], (0.0, 1.0))
var_bounds = garch.variance_bounds(self.resids)
backcast = garch.backcast(self.resids)
parameters = np.array([.1, .1, .8])
names = garch.parameter_names()
names_target = ['omega', 'gamma[1]', 'beta[1]']
assert_equal(names, names_target)
garch.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
0, 1, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
A, b = garch.constraints()
A_target = np.vstack((np.eye(3), np.array([[0, -0.5, -1.0]])))
b_target = np.array([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 = garch.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 = 0.5 * initial_value if t == 0 else \
data[t - 1] ** 2.0 * (data[t - 1] < 0)
sigma2[t] += parameters[1] * shock
lagged_value = initial_value if t == 0 else sigma2[t - 1]
sigma2[t] += parameters[2] * lagged_value
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))
assert_equal(garch.p, 0)
assert_equal(garch.o, 1)
assert_equal(garch.q, 1)
assert_equal(garch.num_params, 3)
assert_equal(garch.name, 'GJR-GARCH')
def test_garch(self):
garch = GARCH()
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.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))
assert_equal(bounds[2], (0.0, 1.0))
backcast = garch.backcast(self.resids)
w = 0.94**np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75]**2) * (w / w.sum())))
var_bounds = garch.variance_bounds(self.resids)
parameters = np.array([.1, .1, .8])
garch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters, self.resids**2.0, np.sign(self.resids),
cond_var_direct, 1, 0, 1, self.T, backcast,
var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
A, b = garch.constraints()
A_target = np.vstack((np.eye(3), np.array([[0, -1.0, -1.0]])))
b_target = np.array([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 = garch.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
lagged_value = initial_value if t == 0 else sigma2[t - 1]
sigma2[t] += parameters[2] * lagged_value
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data / sim_data[0], np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = garch.parameter_names()
names_target = ['omega', 'alpha[1]', 'beta[1]']
assert_equal(names, names_target)
assert_equal(garch.name, 'GARCH')
assert_equal(garch.num_params, 3)
assert_equal(garch.power, 2.0)
assert_equal(garch.p, 1)
assert_equal(garch.o, 0)
assert_equal(garch.q, 1)
def test_garch_power(self):
garch = GARCH(power=1.0)
assert_equal(garch.num_params, 3)
assert_equal(garch.name, 'AVGARCH')
assert_equal(garch.power, 1.0)
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(np.abs(self.resids))))
assert_equal(bounds[1], (0.0, 1.0))
assert_equal(bounds[2], (0.0, 1.0))
var_bounds = garch.variance_bounds(self.resids)
backcast = garch.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum(np.abs(self.resids[:75]) * (w / w.sum())))
parameters = np.array([.1, .1, .8])
garch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters,
np.abs(self.resids),
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
cond_var_direct **= 2.0 # Square since recursion does not apply power
assert_allclose(self.sigma2, cond_var_direct)
a, b = garch.constraints()
a_target = np.vstack((np.eye(3), np.array([[0, -1.0, -1.0]])))
b_target = np.array([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 = garch.simulate(parameters, self.T, rng.simulate([]))
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + 500)
initial_value = 1.0
sigma = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
for t in range(self.T + 500):
sigma[t] = parameters[0]
shock = initial_value if t == 0 else np.abs(data[t - 1])
sigma[t] += parameters[1] * shock
lagged_value = initial_value if t == 0 else sigma[t - 1]
sigma[t] += parameters[2] * lagged_value
data[t] = e[t] * sigma[t]
data = data[500:]
sigma2 = sigma[500:] ** 2.0
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_garch_power(self):
garch = GARCH(power=1.0)
assert_equal(garch.num_params, 3)
assert_equal(garch.name, 'AVGARCH')
assert_equal(garch.power, 1.0)
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.bounds(self.resids)
assert_equal(bounds[0], (0.0, 10.0 * np.mean(np.abs(self.resids))))
assert_equal(bounds[1], (0.0, 1.0))
assert_equal(bounds[2], (0.0, 1.0))
var_bounds = garch.variance_bounds(self.resids)
backcast = garch.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum(np.abs(self.resids[:75]) * (w / w.sum())))
parameters = np.array([.1, .1, .8])
garch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters,
np.abs(self.resids),
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
cond_var_direct **= 2.0 # Square since recursion does not apply power
assert_allclose(self.sigma2, cond_var_direct)
A, b = garch.constraints()
A_target = np.vstack((np.eye(3), np.array([[0, -1.0, -1.0]])))
b_target = np.array([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 = garch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
initial_value = 1.0
sigma = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
for t in range(self.T + 500):
sigma[t] = parameters[0]
shock = initial_value if t == 0 else np.abs(data[t - 1])
sigma[t] += parameters[1] * shock
lagged_value = initial_value if t == 0 else sigma[t - 1]
sigma[t] += parameters[2] * lagged_value
data[t] = e[t] * sigma[t]
data = data[500:]
sigma2 = sigma[500:] ** 2.0
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_garch_no_lagged_vol(self):
garch = GARCH(p=1, o=1, q=0)
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.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))
assert_equal(bounds[2], (-1.0, 2.0))
backcast = garch.backcast(self.resids)
parameters = np.array([.5, .25, .5])
var_bounds = garch.variance_bounds(self.resids)
garch.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters, self.resids**2.0, np.sign(self.resids),
cond_var_direct, 1, 1, 0, self.T, backcast,
var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
A, b = garch.constraints()
A_target = np.vstack((np.eye(3), np.array([[0, -1.0, -0.5]])))
A_target[2, 1] = 1.0
b_target = np.array([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 = garch.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
shock = 0.5 * initial_value if t == 0 else \
(data[t - 1] ** 2.0) * (data[t - 1] < 0)
sigma2[t] += parameters[2] * 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))
assert_equal(garch.p, 1)
assert_equal(garch.o, 1)
assert_equal(garch.q, 0)
assert_equal(garch.num_params, 3)
assert_equal(garch.name, 'GJR-GARCH')
def test_ewma_estimated(self):
ewma = EWMAVariance(lam=None)
sv = ewma.starting_values(self.resids)
assert sv == 0.94
assert sv.shape[0] == ewma.num_params
bounds = ewma.bounds(self.resids)
assert len(bounds) == 1
assert bounds == [(0, 1)]
var_bounds = ewma.variance_bounds(self.resids)
backcast = ewma.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([0.9234])
var_bounds = ewma.variance_bounds(self.resids)
ewma.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
cond_var_direct[0] = backcast
parameters = np.array([0, 1-parameters[0], parameters[0]])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
assert_allclose(self.sigma2 / cond_var_direct, np.ones_like(self.sigma2))
names = ewma.parameter_names()
names_target = ['lam']
assert_equal(names, names_target)
a, b = ewma.constraints()
a_target = np.ones((1, 1))
b_target = np.zeros((1,))
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
assert_equal(ewma.num_params, 1)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
def test_ewma_estimated(self):
ewma = EWMAVariance(lam=None)
sv = ewma.starting_values(self.resids)
assert sv == 0.94
assert sv.shape[0] == ewma.num_params
bounds = ewma.bounds(self.resids)
assert len(bounds) == 1
assert bounds == [(0, 1)]
var_bounds = ewma.variance_bounds(self.resids)
backcast = ewma.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([0.9234])
var_bounds = ewma.variance_bounds(self.resids)
ewma.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
cond_var_direct[0] = backcast
parameters = np.array([0, 1-parameters[0], parameters[0]])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
assert_allclose(self.sigma2 / cond_var_direct, np.ones_like(self.sigma2))
names = ewma.parameter_names()
names_target = ['lam']
assert_equal(names, names_target)
a, b = ewma.constraints()
a_target = np.ones((1, 1))
b_target = np.zeros((1,))
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
assert_equal(ewma.num_params, 1)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
def test_ewma_estimated(self):
ewma = EWMAVariance(lam=None)
sv = ewma.starting_values(self.resids)
assert sv == 0.94
assert sv.shape[0] == ewma.num_params
bounds = ewma.bounds(self.resids)
assert len(bounds) == 1
assert bounds == [(0, 1)]
ewma.variance_bounds(self.resids)
backcast = ewma.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([0.9234])
var_bounds = ewma.variance_bounds(self.resids)
ewma.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
cond_var_direct[0] = backcast
parameters = np.array([0, 1 - parameters[0], parameters[0]])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
assert_allclose(self.sigma2 / cond_var_direct, np.ones_like(self.sigma2))
names = ewma.parameter_names()
names_target = ['lam']
assert_equal(names, names_target)
a, b = ewma.constraints()
a_target = np.ones((1, 1))
b_target = np.zeros((1,))
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
assert_equal(ewma.num_params, 1)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
state = self.rng.get_state()
rng = Normal()
rng.random_state.set_state(state)
lam = parameters[-1]
sim_data = ewma.simulate([lam], 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)
sigma2[0] = initial_value
data[0] = np.sqrt(initial_value)
for t in range(1, self.T + 500):
sigma2[t] = lam * sigma2[t - 1] + (1-lam) * data[t - 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))
def test_garch(self):
garch = GARCH()
sv = garch.starting_values(self.resids)
assert_equal(sv.shape[0], garch.num_params)
bounds = garch.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))
assert_equal(bounds[2], (0.0, 1.0))
backcast = garch.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
var_bounds = garch.variance_bounds(self.resids)
parameters = np.array([.1, .1, .8])
garch.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
A, b = garch.constraints()
A_target = np.vstack((np.eye(3), np.array([[0, -1.0, -1.0]])))
b_target = np.array([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 = garch.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
lagged_value = initial_value if t == 0 else sigma2[t - 1]
sigma2[t] += parameters[2] * lagged_value
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data / sim_data[0], np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = garch.parameter_names()
names_target = ['omega', 'alpha[1]', 'beta[1]']
assert_equal(names, names_target)
assert_true(isinstance(garch.__str__(), str))
repr = garch.__repr__()
assert_true(str(hex(id(garch))) in repr)
assert_equal(garch.name, 'GARCH')
assert_equal(garch.num_params, 3)
assert_equal(garch.power, 2.0)
assert_equal(garch.p, 1)
assert_equal(garch.o, 0)
assert_equal(garch.q, 1)