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_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_riskmetrics(self):
rm06 = RiskMetrics2006()
sv = rm06.starting_values(self.resids)
assert_equal(sv.shape[0], rm06.num_params)
bounds = rm06.bounds(self.resids)
assert_equal(len(bounds), 0)
var_bounds = rm06.variance_bounds(self.resids)
backcast = rm06.backcast(self.resids)
assert_equal(backcast.shape[0], 14)
parameters = np.array([])
names = rm06.parameter_names()
names_target = []
assert_equal(names, names_target)
# TODO: Test variance fit by RM06
rm06.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
A, b = rm06.constraints()
A_target = np.empty((0, 0))
b_target = np.empty((0,))
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
# TODO: Test RM06 Simulation
state = np.random.get_state()
rng = Normal()
sim_data = rm06.simulate(parameters, self.T, rng.simulate([]))
assert_equal(rm06.num_params, 0)
assert_equal(rm06.name, 'RiskMetrics2006')
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_riskmetrics(self):
rm06 = RiskMetrics2006()
sv = rm06.starting_values(self.resids)
assert_equal(sv.shape[0], rm06.num_params)
bounds = rm06.bounds(self.resids)
assert_equal(len(bounds), 0)
var_bounds = rm06.variance_bounds(self.resids)
backcast = rm06.backcast(self.resids)
assert_equal(backcast.shape[0], 14)
parameters = np.array([])
names = rm06.parameter_names()
names_target = []
assert_equal(names, names_target)
# TODO: Test variance fit by RM06
rm06.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
A, b = rm06.constraints()
A_target = np.empty((0, 0))
b_target = np.empty((0, ))
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
# TODO: Test RM06 Simulation
state = np.random.get_state()
rng = Normal()
sim_data = rm06.simulate(parameters, self.T, rng.simulate([]))
assert_equal(rm06.num_params, 0)
assert_equal(rm06.name, 'RiskMetrics2006')
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_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_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_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_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_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')
def test_empty_mean(self):
mod = HARX(self.y, None, None, False, volatility=ConstantVariance(),
distribution=Normal())
res = mod.fit()
mod = ZeroMean(self.y, volatility=ConstantVariance(), distribution=Normal())
res_z = mod.fit()
assert res.num_params == res_z.num_params
assert_series_equal(res.params, res_z.params)
assert res.loglikelihood == res_z.loglikelihood
def test_constant_variance(self):
cv = ConstantVariance()
sv = cv.starting_values(self.resids)
assert_equal(sv.shape[0], cv.num_params)
bounds = cv.bounds(self.resids)
mean_square = np.mean(self.resids ** 2.0)
assert_almost_equal(bounds[0],
(self.resid_var / 100000.0, 10.0 * mean_square))
backcast = cv.backcast(self.resids)
var_bounds = cv.variance_bounds(self.resids)
assert_almost_equal(self.resid_var, backcast)
parameters = np.array([self.resid_var])
cv.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
assert_allclose(np.ones_like(self.sigma2) * self.resid_var,
self.sigma2)
a, b = cv.constraints()
a_target = np.eye(1)
b_target = np.array([0.0])
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 = cv.simulate(parameters, self.T, rng.simulate([]))
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + 500)
sigma2 = np.zeros(self.T + 500)
sigma2[:] = parameters[0]
data = np.zeros(self.T + 500)
data[:] = np.sqrt(sigma2) * e
data = data[500:]
sigma2 = sigma2[500:]
names = cv.parameter_names()
names_target = ['sigma2']
assert_equal(names, names_target)
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(cv.num_params, 1)
assert_equal(cv.name, 'Constant Variance')
assert isinstance(cv.__str__(), str)
txt = cv.__repr__()
assert str(hex(id(cv))) in txt
def test_constant_variance(self):
cv = ConstantVariance()
sv = cv.starting_values(self.resids)
assert_equal(sv.shape[0], cv.num_params)
bounds = cv.bounds(self.resids)
mean_square = np.mean(self.resids ** 2.0)
assert_almost_equal(bounds[0],
(self.resid_var / 100000.0, 10.0 * mean_square))
backcast = cv.backcast(self.resids)
var_bounds = cv.variance_bounds(self.resids)
assert_almost_equal(self.resid_var, backcast)
parameters = np.array([self.resid_var])
cv.compute_variance(parameters, self.resids, self.sigma2, backcast,
var_bounds)
assert_allclose(np.ones_like(self.sigma2) * self.resid_var,
self.sigma2)
A, b = cv.constraints()
A_target = np.eye(1)
b_target = np.array([0.0])
assert_array_equal(A, A_target)
assert_array_equal(b, b_target)
state = np.random.get_state()
rng = Normal()
sim_data = cv.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
sigma2 = np.zeros(self.T + 500)
sigma2[:] = parameters[0]
data = np.zeros(self.T + 500)
data[:] = np.sqrt(sigma2) * e
data = data[500:]
sigma2 = sigma2[500:]
names = cv.parameter_names()
names_target = ['sigma2']
assert_equal(names, names_target)
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(cv.num_params, 1)
assert_equal(cv.name, 'Constant Variance')
assert_true(isinstance(cv.__str__(), str))
repr = cv.__repr__()
assert_true(str(hex(id(cv))) in repr)
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_errors(self):
with pytest.raises(ValueError):
ARX(self.y, lags=np.array([[1, 2], [3, 4]]))
x = self.rng.randn(self.y.shape[0] + 1, 1)
with pytest.raises(ValueError):
ARX(self.y, x=x)
with pytest.raises(ValueError):
HARX(self.y, lags=np.eye(3))
with pytest.raises(ValueError):
ARX(self.y, lags=-1)
with pytest.raises(ValueError):
ARX(self.y, x=self.rng.randn(1, 1), lags=-1)
ar = ARX(self.y, lags=1)
with self.assertRaises(ValueError):
d = Normal()
ar.volatility = d
with self.assertRaises(ValueError):
v = GARCH()
ar.distribution = v
x = self.rng.randn(1000, 1)
with pytest.raises(ValueError):
ar.simulate(np.ones(5), 100, x=x)
with pytest.raises(ValueError):
ar.simulate(np.ones(5), 100)
with pytest.raises(ValueError):
ar.simulate(np.ones(3), 100, initial_value=self.rng.randn(10))
with self.assertRaises(ValueError):
ar.volatility = ConstantVariance()
ar.fit(cov_type='unknown')
def test_normal(self):
dist = Normal()
ll1 = dist.loglikelihoood([], self.resids, self.sigma2)
scipy_dist = stats.norm
ll2 = scipy_dist.logpdf(self.resids, scale=np.sqrt(self.sigma2)).sum()
assert_almost_equal(ll1, ll2)
assert_equal(dist.num_params, 0)
bounds = dist.bounds(self.resids)
assert_equal(len(bounds), 0)
a, b = dist.constraints()
assert_equal(len(a), 0)
assert_array_equal(dist.starting_values(self.resids), np.empty((0,)))
def setup_class(cls):
cls.rng = RandomState(1234)
cls.T = 1000
cls.resids = cls.rng.standard_normal(cls.T)
zm = ZeroMean()
zm.volatility = GARCH()
seed = 12345
random_state = np.random.RandomState(seed)
zm.distribution = Normal(random_state=random_state)
sim_data = zm.simulate(np.array([0.1, 0.1, 0.8]), 1000)
with pytest.raises(ValueError):
zm.simulate(np.array([0.1, 0.1, 0.8]), 1000, initial_value=3.0)
date_index = pd.date_range("2000-12-31", periods=1000, freq="W")
cls.y = sim_data.data.values
cls.y_df = pd.DataFrame(
cls.y[:, None], columns=["LongVariableName"], index=date_index
)
cls.y_series = pd.Series(
cls.y, name="VeryVeryLongLongVariableName", index=date_index
)
x = cls.resids + cls.rng.standard_normal(cls.T)
cls.x = x[:, None]
cls.x_df = pd.DataFrame(cls.x, columns=["LongExogenousName"])
cls.resid_var = np.var(cls.resids)
cls.sigma2 = np.zeros_like(cls.resids)
cls.backcast = 1.0
def test_fixed_variance(self):
variance = np.arange(1000.0) + 1.0
fv = FixedVariance(variance)
fv.start, fv.stop = 0, 1000
parameters = np.array([2.0])
resids = self.resids
sigma2 = np.empty_like(resids)
backcast = fv.backcast(resids)
var_bounds = fv.variance_bounds(resids, 2.0)
fv.compute_variance(parameters, resids, sigma2, backcast, var_bounds)
sv = fv.starting_values(resids)
cons = fv.constraints()
bounds = fv.bounds(resids)
assert_allclose(sigma2, 2.0 * variance)
assert_allclose(sv, (resids / np.sqrt(variance)).var())
assert var_bounds.shape == (resids.shape[0], 2)
assert fv.num_params == 1
assert fv.parameter_names() == ['scale']
assert fv.name == 'Fixed Variance'
assert_equal(cons[0], np.ones((1, 1)))
assert_equal(cons[1], np.zeros(1))
assert_equal(bounds[0][0], sv[0] / 100000.0)
sigma2 = np.empty(500)
fv.start = 250
fv.stop = 750
fv.compute_variance(parameters, resids[250:750], sigma2, backcast,
var_bounds)
assert_allclose(sigma2, 2.0 * variance[250:750])
fv = FixedVariance(variance, unit_scale=True)
fv.start, fv.stop = 0, 1000
sigma2 = np.empty_like(resids)
parameters = np.empty(0)
fv.compute_variance(parameters, resids, sigma2, backcast, var_bounds)
sv = fv.starting_values(resids)
cons = fv.constraints()
bounds = fv.bounds(resids)
assert_allclose(sigma2, variance)
assert_allclose(sv, np.empty(0))
assert fv.num_params == 0
assert fv.parameter_names() == []
assert fv.name == 'Fixed Variance (Unit Scale)'
assert_equal(cons[0], np.empty((0, 0)))
assert_equal(cons[1], np.empty((0)))
assert bounds == []
rng = Normal()
with pytest.raises(NotImplementedError):
fv.simulate(parameters, 1000, rng)
fv = FixedVariance(variance, unit_scale=True)
fv.start, fv.stop = 123, 731
sigma2 = np.empty_like(resids)
parameters = np.empty(0)
assert fv.start == 123
assert fv.stop == 731
with pytest.raises(ValueError):
fv.compute_variance(parameters, resids, sigma2, backcast,
var_bounds)
def test_autoscale():
rs = np.random.RandomState(34254321)
dist = Normal(random_state=rs)
am = arch_model(None)
am.distribution = dist
data = am.simulate([0, 0.0001, 0.05, 0.94], nobs=1000)
am = arch_model(data.data)
with pytest.warns(DataScaleWarning):
res = am.fit(disp=DISPLAY)
assert_almost_equal(res.scale, 1.0)
am = arch_model(data.data, rescale=True)
res_auto = am.fit(disp=DISPLAY)
assert_almost_equal(res_auto.scale, 10.0)
am = arch_model(10 * data.data)
res_manual = am.fit(disp=DISPLAY)
assert_series_equal(res_auto.params, res_manual.params)
res_no = arch_model(data.data, rescale=False).fit(disp=DISPLAY)
assert res_no.scale == 1.0
am = arch_model(10000 * data.data, rescale=True)
res_big = am.fit(disp=DISPLAY)
assert_almost_equal(res_big.scale, 0.1)
def test_invalid_params():
pits = np.arange(1, 100.0) / 100.0
dist = Normal()
with pytest.raises(ValueError):
dist.ppf(pits, [1.0])
dist = StudentsT()
with pytest.raises(ValueError):
dist.ppf(pits, [1.0])
def test_invalid_params():
pits = np.arange(1, 100.0) / 100.0
dist = Normal()
with pytest.raises(ValueError):
dist.ppf(pits, [1.0])
dist = StudentsT()
with pytest.raises(ValueError):
dist.ppf(pits, [1.0])
def test_optimization_options(self):
norm = Normal(random_state=RandomState([12891298, 843084]))
am = arch_model(None)
am.distribution = norm
data = am.simulate(np.array([0.0, 0.1, 0.1, 0.85]), 2500)
am = arch_model(data.data)
std = am.fit(disp=DISPLAY)
loose = am.fit(tol=1e-2, disp=DISPLAY)
assert std.loglikelihood >= loose.loglikelihood
with warnings.catch_warnings(record=True) as w:
short = am.fit(options={"maxiter": 3}, disp=DISPLAY)
assert len(w) == 1
assert std.loglikelihood >= short.loglikelihood
assert short.convergence_flag != 0
def test_normal(self):
dist = Normal()
ll1 = dist.loglikelihood([], self.resids, self.sigma2)
scipy_dist = stats.norm
ll2 = scipy_dist.logpdf(self.resids, scale=np.sqrt(self.sigma2)).sum()
assert_almost_equal(ll1, ll2)
assert_equal(dist.num_params, 0)
bounds = dist.bounds(self.resids)
assert_equal(len(bounds), 0)
a, b = dist.constraints()
assert_equal(len(a), 0)
assert_array_equal(dist.starting_values(self.resids), np.empty((0, )))
def test_cgarch(self):
cgarch = CGARCH()
sv = cgarch.starting_values(self.resids)
assert_equal(sv.shape[0], cgarch.num_params)
parameters = np.array([0.1, 0.4, 0.06, 0.8, 0.2])
bounds = cgarch.bounds(self.resids)
assert_equal(bounds[0], (0, 1))
assert_equal(bounds[1], (0, 1))
assert_equal(bounds[2], (0, 1))
assert_equal(bounds[3], (0.79, 1))
assert_equal(bounds[4], (0, 1))
backcast = cgarch.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
var_bounds = cgarch.variance_bounds(self.resids)
cgarch.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
g2 = np.ndarray(self.T)
q2 = g2.copy()
rec.cgarch_recursion(parameters,
self.resids ** 2.0,
cond_var_direct,
backcast,
var_bounds, g2, q2)
assert_allclose(self.sigma2, cond_var_direct)
a, b = cgarch.constraints()
a_target = np.array([[0, 1, 0, 0, -1], [-1, -1, 0, 1, 0], [0, 0, 0, -1, 0]])
b_target = np.array([0, 0, -1])
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
# test simulated data
state = np.random.get_state()
rng = Normal()
sim_data = cgarch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
alpha, beta, omega, rho, phi = parameters
converted_params = cgarch._covertparams(parameters)
fromgarch = converted_params[0]/(1-(np.sum(converted_params[1:])))
fromcg = omega/(1-rho)
aver = (fromcg + fromgarch)/2
if (aver > 0.0) and (aver < 0.2):
initial_value = aver
else:
initial_value = 0.1
sigma2 = np.zeros(self.T + 500)
sigma2[0] = initial_value
g2 = np.ndarray(self.T + 500)
q2 = g2.copy()
q2[0] = initial_value * 0.65
g2[0] = initial_value - q2[0]
data = np.zeros(self.T + 500)
data[0] = e[0] * np.sqrt(sigma2[0])
for i in range(1, self.T + 500):
g2[i] = alpha * (data[i - 1]**2 - q2[i - 1]) + beta * g2[i - 1]
q2[i] = omega + rho * q2[i - 1] + phi * (data[i - 1]**2 - sigma2[i - 1])
sigma2[i] = g2[i] + q2[i]
data[i] = e[i] * (np.sqrt(sigma2[i]))
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 = cgarch.parameter_names()
names_target = ["alpha", "beta", "omega", "rho", "phi"]
assert_equal(names, names_target)
assert isinstance(cgarch.__str__(), str)
assert_equal(cgarch.name, 'ComponentGARCH')
assert_equal(cgarch.num_params, 5)
assert_equal(cgarch.p, 2)
assert_equal(cgarch.q, 2)
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_harch(self):
harch = HARCH(lags=[1, 5, 22])
sv = harch.starting_values(self.resids)
assert_equal(sv.shape[0], harch.num_params)
bounds = harch.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))
assert_equal(bounds[3], (0.0, 1.0))
var_bounds = harch.variance_bounds(self.resids)
backcast = harch.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([.1, .4, .3, .2])
var_bounds = harch.variance_bounds(self.resids)
harch.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
lags = np.array([1, 5, 22], dtype=np.int32)
rec.harch_recursion(parameters,
self.resids,
cond_var_direct,
lags,
self.T,
backcast,
var_bounds)
names = harch.parameter_names()
names_target = ['omega', 'alpha[1]', 'alpha[5]', 'alpha[22]']
assert_equal(names, names_target)
assert_allclose(self.sigma2, cond_var_direct)
a, b = harch.constraints()
a_target = np.vstack((np.eye(4), np.array([[0, -1.0, -1.0, -1.0]])))
b_target = np.array([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 = harch.simulate(parameters, self.T, rng.simulate([]))
np.random.set_state(state)
e = np.random.standard_normal(self.T + 500)
sigma2 = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
lagged = np.zeros(22)
for t in range(self.T + 500):
sigma2[t] = parameters[0]
lagged[:] = backcast
if t > 0:
if t == 1:
lagged[0] = data[0] ** 2.0
elif t < 22:
lagged[:t] = data[t - 1::-1] ** 2.0
else:
lagged = data[t - 1:t - 22:-1] ** 2.0
shock1 = data[t - 1] ** 2.0 if t > 0 else backcast
if t >= 5:
shock5 = np.mean(data[t - 5:t] ** 2.0)
else:
shock5 = 0.0
for i in range(5):
shock5 += data[t - i - 1] if t - i - 1 >= 0 else backcast
shock5 = shock5 / 5.0
if t >= 22:
shock22 = np.mean(data[t - 22:t] ** 2.0)
else:
shock22 = 0.0
for i in range(22):
shock22 += data[t - i - 1] if t - i - 1 >= 0 else backcast
shock22 = shock22 / 22.0
sigma2[t] += parameters[1] * shock1 + parameters[2] * shock5 + parameters[3] * shock22
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(harch.name, 'HARCH')
assert_equal(harch.lags, [1, 5, 22])
assert_equal(harch.num_params, 4)
assert isinstance(harch.__str__(), str)
txt = harch.__repr__()
assert str(hex(id(harch))) in txt
def arch_model(
y: Optional[ArrayLike],
x: Optional[ArrayLike] = None,
mean: str = "Constant",
lags: Optional[Union[int, List[int], NDArray]] = 0,
vol: str = "Garch",
p: Union[int, List[int]] = 1,
o: int = 0,
q: int = 1,
power: float = 2.0,
dist: str = "Normal",
hold_back: Optional[int] = None,
rescale: Optional[bool] = None,
) -> HARX:
"""
Initialization of common ARCH model specifications
Parameters
----------
y : {ndarray, Series, None}
The dependent variable
x : {np.array, DataFrame}, optional
Exogenous regressors. Ignored if model does not permit exogenous
regressors.
mean : str, optional
Name of the mean model. Currently supported options are: 'Constant',
'Zero', 'LS', 'AR', 'ARX', 'HAR' and 'HARX'
lags : int or list (int), optional
Either a scalar integer value indicating lag length or a list of
integers specifying lag locations.
vol : str, optional
Name of the volatility model. Currently supported options are:
'GARCH' (default), 'ARCH', 'EGARCH', 'FIARCH' and 'HARCH'
p : int, optional
Lag order of the symmetric innovation
o : int, optional
Lag order of the asymmetric innovation
q : int, optional
Lag order of lagged volatility or equivalent
power : float, optional
Power to use with GARCH and related models
dist : int, optional
Name of the error distribution. Currently supported options are:
* Normal: 'normal', 'gaussian' (default)
* Students's t: 't', 'studentst'
* Skewed Student's t: 'skewstudent', 'skewt'
* Generalized Error Distribution: 'ged', 'generalized error"
hold_back : int
Number of observations at the start of the sample to exclude when
estimating model parameters. Used when comparing models with different
lag lengths to estimate on the common sample.
rescale : bool
Flag indicating whether to automatically rescale data if the scale
of the data is likely to produce convergence issues when estimating
model parameters. If False, the model is estimated on the data without
transformation. If True, than y is rescaled and the new scale is
reported in the estimation results.
Returns
-------
model : ARCHModel
Configured ARCH model
Examples
--------
>>> import datetime as dt
>>> import pandas_datareader.data as web
>>> djia = web.get_data_fred('DJIA')
>>> returns = 100 * djia['DJIA'].pct_change().dropna()
A basic GARCH(1,1) with a constant mean can be constructed using only
the return data
>>> from arch.univariate import arch_model
>>> am = arch_model(returns)
Alternative mean and volatility processes can be directly specified
>>> am = arch_model(returns, mean='AR', lags=2, vol='harch', p=[1, 5, 22])
This example demonstrates the construction of a zero mean process
with a TARCH volatility process and Student t error distribution
>>> am = arch_model(returns, mean='zero', p=1, o=1, q=1,
... power=1.0, dist='StudentsT')
Notes
-----
Input that are not relevant for a particular specification, such as `lags`
when `mean='zero'`, are silently ignored.
"""
known_mean = ("zero", "constant", "harx", "har", "ar", "arx", "ls")
known_vol = ("arch", "figarch", "garch", "harch", "constant", "egarch")
known_dist = (
"normal",
"gaussian",
"studentst",
"t",
"skewstudent",
"skewt",
"ged",
"generalized error",
)
mean = mean.lower()
vol = vol.lower()
dist = dist.lower()
if mean not in known_mean:
raise ValueError("Unknown model type in mean")
if vol.lower() not in known_vol:
raise ValueError("Unknown model type in vol")
if dist.lower() not in known_dist:
raise ValueError("Unknown model type in dist")
if mean == "harx":
am = HARX(y, x, lags, hold_back=hold_back, rescale=rescale)
elif mean == "har":
am = HARX(y, None, lags, hold_back=hold_back, rescale=rescale)
elif mean == "arx":
am = ARX(y, x, lags, hold_back=hold_back, rescale=rescale)
elif mean == "ar":
am = ARX(y, None, lags, hold_back=hold_back, rescale=rescale)
elif mean == "ls":
am = LS(y, x, hold_back=hold_back, rescale=rescale)
elif mean == "constant":
am = ConstantMean(y, hold_back=hold_back, rescale=rescale)
else: # mean == "zero"
am = ZeroMean(y, hold_back=hold_back, rescale=rescale)
if vol in ("arch", "garch", "figarch",
"egarch") and not isinstance(p, int):
raise TypeError(
"p must be a scalar int for all volatility processes except HARCH."
)
if vol == "constant":
v: VolatilityProcess = ConstantVariance()
elif vol == "arch":
assert isinstance(p, int)
v = ARCH(p=p)
elif vol == "figarch":
assert isinstance(p, int)
v = FIGARCH(p=p, q=q)
elif vol == "garch":
assert isinstance(p, int)
v = GARCH(p=p, o=o, q=q, power=power)
elif vol == "egarch":
assert isinstance(p, int)
v = EGARCH(p=p, o=o, q=q)
else: # vol == 'harch'
v = HARCH(lags=p)
if dist in ("skewstudent", "skewt"):
d: Distribution = SkewStudent()
elif dist in ("studentst", "t"):
d = StudentsT()
elif dist in ("ged", "generalized error"):
d = GeneralizedError()
else: # ('gaussian', 'normal')
d = Normal()
am.volatility = v
am.distribution = d
return am
def test_bad_input():
with pytest.raises(TypeError):
Normal(random_state="random_state")
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)
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 arch_model(y,
x=None,
mean='Constant',
lags=0,
vol='Garch',
p=1,
o=0,
q=1,
power=2.0,
dist='Normal',
hold_back=None):
"""
Convenience function to simplify initialization of ARCH models
Parameters
----------
y : {ndarray, Series, None}
The dependent variable
x : {np.array, DataFrame}, optional
Exogenous regressors. Ignored if model does not permit exogenous
regressors.
mean : str, optional
Name of the mean model. Currently supported options are: 'Constant',
'Zero', 'ARX' and 'HARX'
lags : int or list (int), optional
Either a scalar integer value indicating lag length or a list of
integers specifying lag locations.
vol : str, optional
Name of the volatility model. Currently supported options are:
'GARCH' (default), "EGARCH', 'ARCH' and 'HARCH'
p : int, optional
Lag order of the symmetric innovation
o : int, optional
Lag order of the asymmetric innovation
q : int, optional
Lag order of lagged volatility or equivalent
power : float, optional
Power to use with GARCH and related models
dist : int, optional
Name of the error distribution. Currently supported options are:
* Normal: 'normal', 'gaussian' (default)
* Students's t: 't', 'studentst'
* Skewed Student's t: 'skewstudent', 'skewt'
* Generalized Error Distribution: 'ged', 'generalized error"
hold_back : int
Number of observations at the start of the sample to exclude when
estimating model parameters. Used when comparing models with different
lag lengths to estimate on the common sample.
Returns
-------
model : ARCHModel
Configured ARCH model
Examples
--------
>>> import datetime as dt
>>> import pandas_datareader.data as web
>>> djia = web.get_data_fred('DJIA')
>>> returns = 100 * djia['DJIA'].pct_change().dropna()
A basic GARCH(1,1) with a constant mean can be constructed using only
the return data
>>> from arch.univariate import arch_model
>>> am = arch_model(returns)
Alternative mean and volatility processes can be directly specified
>>> am = arch_model(returns, mean='AR', lags=2, vol='harch', p=[1, 5, 22])
This example demonstrates the construction of a zero mean process
with a TARCH volatility process and Student t error distribution
>>> am = arch_model(returns, mean='zero', p=1, o=1, q=1,
... power=1.0, dist='StudentsT')
Notes
-----
Input that are not relevant for a particular specification, such as `lags`
when `mean='zero'`, are silently ignored.
"""
known_mean = ('zero', 'constant', 'harx', 'har', 'ar', 'arx', 'ls')
known_vol = ('arch', 'garch', 'harch', 'constant', 'egarch')
known_dist = ('normal', 'gaussian', 'studentst', 't', 'skewstudent',
'skewt', 'ged', 'generalized error')
mean = mean.lower()
vol = vol.lower()
dist = dist.lower()
if mean not in known_mean:
raise ValueError('Unknown model type in mean')
if vol.lower() not in known_vol:
raise ValueError('Unknown model type in vol')
if dist.lower() not in known_dist:
raise ValueError('Unknown model type in dist')
if mean == 'zero':
am = ZeroMean(y, hold_back=hold_back)
elif mean == 'constant':
am = ConstantMean(y, hold_back=hold_back)
elif mean == 'harx':
am = HARX(y, x, lags, hold_back=hold_back)
elif mean == 'har':
am = HARX(y, None, lags, hold_back=hold_back)
elif mean == 'arx':
am = ARX(y, x, lags, hold_back=hold_back)
elif mean == 'ar':
am = ARX(y, None, lags, hold_back=hold_back)
else:
am = LS(y, x, hold_back=hold_back)
if vol == 'constant':
v = ConstantVariance()
elif vol == 'arch':
v = ARCH(p=p)
elif vol == 'garch':
v = GARCH(p=p, o=o, q=q, power=power)
elif vol == 'egarch':
v = EGARCH(p=p, o=o, q=q)
else: # vol == 'harch'
v = HARCH(lags=p)
if dist in ('skewstudent', 'skewt'):
d = SkewStudent()
elif dist in ('studentst', 't'):
d = StudentsT()
elif dist in ('ged', 'generalized error'):
d = GeneralizedError()
else: # ('gaussian', 'normal')
d = Normal()
am.volatility = v
am.distribution = d
return am
def test_harch(self):
harch = HARCH(lags=[1, 5, 22])
sv = harch.starting_values(self.resids)
assert_equal(sv.shape[0], harch.num_params)
bounds = harch.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))
assert_equal(bounds[3], (0.0, 1.0))
var_bounds = harch.variance_bounds(self.resids)
backcast = harch.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([.1, .4, .3, .2])
var_bounds = harch.variance_bounds(self.resids)
harch.compute_variance(parameters, self.resids, self.sigma2,
backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
lags = np.array([1, 5, 22], dtype=np.int32)
rec.harch_recursion(parameters,
self.resids,
cond_var_direct,
lags,
self.T,
backcast,
var_bounds)
names = harch.parameter_names()
names_target = ['omega', 'alpha[1]', 'alpha[5]', 'alpha[22]']
assert_equal(names, names_target)
assert_allclose(self.sigma2, cond_var_direct)
A, b = harch.constraints()
A_target = np.vstack((np.eye(4), np.array([[0, -1.0, -1.0, -1.0]])))
b_target = np.array([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 = harch.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)
lagged = np.zeros(22)
for t in range(self.T + 500):
sigma2[t] = parameters[0]
lagged[:] = backcast
if t > 0:
if t == 1:
lagged[0] = data[0] ** 2.0
elif t < 22:
lagged[:t] = data[t - 1::-1] ** 2.0
else:
lagged = data[t - 1:t - 22:-1] ** 2.0
shock1 = data[t - 1] ** 2.0 if t > 0 else backcast
if t >= 5:
shock5 = np.mean(data[t - 5:t] ** 2.0)
else:
shock5 = 0.0
for i in range(5):
shock5 += data[t - i - 1] if t - i - 1 >= 0 else backcast
shock5 = shock5 / 5.0
if t >= 22:
shock22 = np.mean(data[t - 22:t] ** 2.0)
else:
shock22 = 0.0
for i in range(22):
shock22 += data[t - i - 1] if t - i - 1 >= 0 else backcast
shock22 = shock22 / 22.0
sigma2[t] += parameters[1] * shock1 \
+ parameters[2] * shock5 \
+ parameters[3] * shock22
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(harch.name, 'HARCH')
assert_equal(harch.lags, [1, 5, 22])
assert_equal(harch.num_params, 4)
def simulated_data(request):
rs = np.random.RandomState(1)
zm = ZeroMean(volatility=GARCH(), distribution=Normal(rs))
sim_data = zm.simulate(np.array([0.1, 0.1, 0.88]), 1000)
return np.asarray(sim_data.data) if request.param else sim_data.data
def test_midas_symmetric(self):
midas = MIDASHyperbolic()
sv = midas.starting_values(self.resids)
assert_equal(sv.shape[0], midas.num_params)
bounds = midas.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 = midas.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast, np.sum((self.resids[:75] ** 2) * (w / w.sum())))
var_bounds = midas.variance_bounds(self.resids)
parameters = np.array([.1, .9, .4])
midas.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
weights = midas._weights(parameters)
theta = parameters[-1]
j = np.arange(1, 22 + 1)
direct_weights = gamma(j + theta) / (gamma(j+1)*gamma(theta))
direct_weights = direct_weights / direct_weights.sum()
assert_allclose(weights, direct_weights)
resids = self.resids
direct_params = parameters.copy()
direct_params[-1] = 0.0 # gamma, strip theta
rec.midas_recursion_python(direct_params, weights, resids, cond_var_direct, self.T,
backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
a, b = midas.constraints()
a_target = np.zeros((5, 3))
a_target[0, 0] = 1
a_target[1, 1] = 1
a_target[2, 1] = -1
a_target[3, 2] = 1
a_target[4, 2] = -1
b_target = np.array([0.0, 0.0, -1.0, 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 = midas.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[:22] = initial_value
omega, alpha = parameters[:2]
for t in range(22, self.T + 500):
sigma2[t] = omega
for i in range(22):
shock = initial_value if t - i - 1 < 22 else data[t - i - 1] ** 2.0
sigma2[t] += alpha * weights[i] * shock
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
assert_almost_equal(data / sim_data[0], np.ones_like(data))
names = midas.parameter_names()
names_target = ['omega', 'alpha', 'theta']
assert_equal(names, names_target)
assert isinstance(midas.__str__(), str)
txt = midas.__repr__()
assert str(hex(id(midas))) in txt
assert_equal(midas.name, 'MIDAS Hyperbolic')
assert_equal(midas.num_params, 3)
assert_equal(midas.m, 22)
with pytest.warns(InitialValueWarning):
parameters = np.array([.1, 1.1, .4])
midas.simulate(parameters, self.T, rng.simulate([]))
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 isinstance(garch.__str__(), str)
txt = garch.__repr__()
assert str(hex(id(garch))) in txt
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 simulated_data():
rs = np.random.RandomState(1)
zm = ZeroMean(volatility=GARCH(), distribution=Normal(rs))
sim_data = zm.simulate(np.array([0.1, 0.1, 0.88]), 1000)
return sim_data.data
def test_midas_asymmetric(self):
midas = MIDASHyperbolic(33, asym=True)
sv = midas.starting_values(self.resids)
assert_equal(sv.shape[0], midas.num_params)
bounds = midas.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))
assert_equal(bounds[3], (0.0, 1.0))
backcast = midas.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast, np.sum((self.resids[:75] ** 2) * (w / w.sum())))
var_bounds = midas.variance_bounds(self.resids)
parameters = np.array([.1, .3, 1.2, .4])
midas.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
weights = midas._weights(parameters)
wlen = len(weights)
theta = parameters[-1]
j = np.arange(1, wlen+1)
direct_weights = gammaln(j + theta) - gammaln(j + 1) - gammaln(theta)
direct_weights = np.exp(direct_weights)
direct_weights = direct_weights/direct_weights.sum()
assert_allclose(direct_weights, weights)
resids = self.resids
direct_params = parameters[:3].copy()
rec.midas_recursion_python(direct_params, weights, resids, cond_var_direct, self.T,
backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
a, b = midas.constraints()
a_target = np.zeros((5, 4))
a_target[0, 0] = 1
a_target[1, 1] = 1
a_target[1, 2] = 1
a_target[2, 1] = -1
a_target[2, 2] = -0.5
a_target[3, 3] = 1
a_target[4, 3] = -1
b_target = np.array([0.0, 0.0, -1.0, 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)
burn = wlen
sim_data = midas.simulate(parameters, self.T, rng.simulate([]), burn=burn)
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + burn)
initial_value = 1.0
sigma2 = np.zeros(self.T + burn)
data = np.zeros(self.T + burn)
sigma2[:wlen] = initial_value
omega, alpha, gamma = parameters[:3]
for t in range(wlen, self.T + burn):
sigma2[t] = omega
for i in range(wlen):
if t - i - 1 < wlen:
shock = initial_value
coeff = (alpha + 0.5 * gamma) * weights[i]
else:
shock = data[t - i - 1] ** 2.0
coeff = (alpha + gamma * (data[t - i - 1] < 0)) * weights[i]
sigma2[t] += coeff * shock
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[burn:]
sigma2 = sigma2[burn:]
assert_almost_equal(data / sim_data[0], np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
names = midas.parameter_names()
names_target = ['omega', 'alpha', 'gamma', 'theta']
assert_equal(names, names_target)
assert isinstance(midas.__str__(), str)
txt = midas.__repr__()
assert str(hex(id(midas))) in txt
assert_equal(midas.name, 'MIDAS Hyperbolic')
assert_equal(midas.num_params, 4)
assert_equal(midas.m, 33)
with pytest.warns(InitialValueWarning):
parameters = np.array([.1, .3, 1.6, .4])
midas.simulate(parameters, self.T, rng.simulate([]))
def __init__(self, random_state=None):
DistributionMixin.__init__(self)
N.__init__(self, random_state)
