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_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)