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_no_param_volatility(self):
cm = ConstantMean(self.y)
cm.volatility = EWMAVariance()
cm.fit(update_freq=0, disp=DISPLAY)
cm.volatility = RiskMetrics2006()
cm.fit(update_freq=0, disp=DISPLAY)
ar = ARX(self.y, lags=5)
ar.volatility = EWMAVariance()
ar.fit(update_freq=0, disp=DISPLAY)
ar.volatility = RiskMetrics2006()
ar.fit(update_freq=0, disp=DISPLAY)
assert 'tau0' in str(ar.volatility)
assert 'tau1' in str(ar.volatility)
assert 'kmax' in str(ar.volatility)
def test_errors(self):
with pytest.raises(ValueError):
GARCH(p=-1)
with pytest.raises(ValueError):
GARCH(o=-1)
with pytest.raises(ValueError):
GARCH(q=-1)
with pytest.raises(ValueError):
GARCH(p=0, q=0)
with pytest.raises(ValueError):
GARCH(power=-0.5)
with pytest.raises(ValueError):
EWMAVariance(lam=-0.5)
with pytest.raises(ValueError):
RiskMetrics2006(tau0=1, tau1=10)
with pytest.raises(ValueError):
RiskMetrics2006(tau0=1, tau1=10)
with pytest.raises(ValueError):
RiskMetrics2006(tau1=-10)
with pytest.raises(ValueError):
RiskMetrics2006(tau0=10, tau1=8, rho=1.5)
with pytest.raises(ValueError):
RiskMetrics2006(kmax=0)
with pytest.raises(ValueError):
RiskMetrics2006(rho=0.5)
def test_ewma_estimated(self):
ewma = EWMAVariance(lam=None)
sv = ewma.starting_values(self.resids)
assert sv == 0.94
assert sv.shape[0] == ewma.num_params
bounds = ewma.bounds(self.resids)
assert len(bounds) == 1
assert bounds == [(0, 1)]
var_bounds = ewma.variance_bounds(self.resids)
backcast = ewma.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
parameters = np.array([0.9234])
var_bounds = ewma.variance_bounds(self.resids)
ewma.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
cond_var_direct[0] = backcast
parameters = np.array([0, 1-parameters[0], parameters[0]])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
assert_allclose(self.sigma2 / cond_var_direct, np.ones_like(self.sigma2))
names = ewma.parameter_names()
names_target = ['lam']
assert_equal(names, names_target)
a, b = ewma.constraints()
a_target = np.ones((1, 1))
b_target = np.zeros((1,))
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
assert_equal(ewma.num_params, 1)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
def test_ewma(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')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
def test_ewma_estimated(self):
ewma = EWMAVariance(lam=None)
sv = ewma.starting_values(self.resids)
assert sv == 0.94
assert sv.shape[0] == ewma.num_params
bounds = ewma.bounds(self.resids)
assert len(bounds) == 1
assert bounds == [(0, 1)]
ewma.variance_bounds(self.resids)
backcast = ewma.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
parameters = np.array([0.9234])
var_bounds = ewma.variance_bounds(self.resids)
ewma.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
cond_var_direct[0] = backcast
parameters = np.array([0, 1 - parameters[0], parameters[0]])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
assert_allclose(self.sigma2 / cond_var_direct, np.ones_like(self.sigma2))
names = ewma.parameter_names()
names_target = ['lam']
assert_equal(names, names_target)
a, b = ewma.constraints()
a_target = np.ones((1, 1))
b_target = np.zeros((1,))
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
assert_equal(ewma.num_params, 1)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
state = self.rng.get_state()
rng = Normal()
rng.random_state.set_state(state)
lam = parameters[-1]
sim_data = ewma.simulate([lam], self.T, rng.simulate([]))
self.rng.set_state(state)
e = self.rng.standard_normal(self.T + 500)
initial_value = 1.0
sigma2 = np.zeros(self.T + 500)
data = np.zeros(self.T + 500)
sigma2[0] = initial_value
data[0] = np.sqrt(initial_value)
for t in range(1, self.T + 500):
sigma2[t] = lam * sigma2[t - 1] + (1-lam) * data[t - 1] ** 2.0
data[t] = e[t] * np.sqrt(sigma2[t])
data = data[500:]
sigma2 = sigma2[500:]
assert_almost_equal(data - sim_data[0] + 1.0, np.ones_like(data))
assert_almost_equal(sigma2 / sim_data[1], np.ones_like(sigma2))
def test_ewma_estimated(self):
ewma = EWMAVariance(lam=None)
sv = ewma.starting_values(self.resids)
assert sv == 0.94
assert sv.shape[0] == ewma.num_params
bounds = ewma.bounds(self.resids)
assert len(bounds) == 1
assert bounds == [(0, 1)]
var_bounds = ewma.variance_bounds(self.resids)
backcast = ewma.backcast(self.resids)
w = 0.94 ** np.arange(75)
assert_almost_equal(backcast,
np.sum((self.resids[:75] ** 2) * (w / w.sum())))
parameters = np.array([0.9234])
var_bounds = ewma.variance_bounds(self.resids)
ewma.compute_variance(parameters, self.resids, self.sigma2, backcast, var_bounds)
cond_var_direct = np.zeros_like(self.sigma2)
cond_var_direct[0] = backcast
parameters = np.array([0, 1-parameters[0], parameters[0]])
rec.garch_recursion(parameters,
self.resids ** 2.0,
np.sign(self.resids),
cond_var_direct,
1, 0, 1, self.T, backcast, var_bounds)
assert_allclose(self.sigma2, cond_var_direct)
assert_allclose(self.sigma2 / cond_var_direct, np.ones_like(self.sigma2))
names = ewma.parameter_names()
names_target = ['lam']
assert_equal(names, names_target)
a, b = ewma.constraints()
a_target = np.ones((1, 1))
b_target = np.zeros((1,))
assert_array_equal(a, a_target)
assert_array_equal(b, b_target)
assert_equal(ewma.num_params, 1)
assert_equal(ewma.name, 'EWMA/RiskMetrics')
assert isinstance(ewma.__str__(), str)
txt = ewma.__repr__()
assert str(hex(id(ewma))) in txt
y[::29] = np.nan
with pytest.raises(ValueError, match="NaN or inf values"):
arch_model(y)
y = np.random.standard_normal(1000)
y[::53] = np.inf
with pytest.raises(ValueError, match="NaN or inf values"):
arch_model(y)
y[::29] = np.nan
y[::53] = np.inf
with pytest.raises(ValueError, match="NaN or inf values"):
arch_model(y)
@pytest.mark.parametrize("first_obs", [None, 250])
@pytest.mark.parametrize("last_obs", [None, 2750])
@pytest.mark.parametrize("vol", [RiskMetrics2006(), EWMAVariance()])
def test_parameterless_fit(first_obs, last_obs, vol):
base = ConstantMean(SP500, volatility=vol)
base_res = base.fit(first_obs=first_obs, last_obs=last_obs, disp="off")
mod = ZeroMean(SP500, volatility=vol)
res = mod.fit(first_obs=first_obs, last_obs=last_obs, disp="off")
assert res.conditional_volatility.shape == base_res.conditional_volatility.shape
def test_invalid_vol_dist():
with pytest.raises(TypeError, match="volatility must inherit"):
ConstantMean(SP500, volatility="GARCH")
with pytest.raises(TypeError, match="distribution must inherit"):
ConstantMean(SP500, distribution="Skew-t")