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)
# 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_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 = 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_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 = 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_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_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_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_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 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_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_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 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 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_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_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_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)
