def test_ar_to_impulse(self):
arp = np.array([0.9])
impulses = _ar_to_impulse(20, arp)
expected = 0.9**np.arange(20)
assert_allclose(impulses, expected)
arp = np.array([0.5, 0.3])
impulses = _ar_to_impulse(20, arp)
comp = np.array([arp, [1, 0]])
a = comp.copy()
expected = np.ones(20)
for i in range(1, 20):
expected[i] = a[0, 0]
a = a.dot(comp)
assert_allclose(impulses, expected)
arp = np.array([1.5, 0.0, -0.7])
impulses = _ar_to_impulse(20, arp)
comp = np.array([arp, [1, 0, 0], [0, 1, 0]])
a = comp.copy()
expected = np.ones(20)
for i in range(1, 20):
expected[i] = a[0, 0]
a = a.dot(comp)
assert_allclose(impulses, expected)
def test_ar_to_impulse(self):
arp = np.array([0.9])
impulses = _ar_to_impulse(20, arp)
expected = 0.9 ** np.arange(20)
assert_allclose(impulses, expected)
arp = np.array([0.5, 0.3])
impulses = _ar_to_impulse(20, arp)
comp = np.array([arp, [1, 0]])
a = comp.copy()
expected = np.ones(20)
for i in range(1, 20):
expected[i] = a[0, 0]
a = a.dot(comp)
assert_allclose(impulses, expected)
arp = np.array([1.5, 0.0, -0.7])
impulses = _ar_to_impulse(20, arp)
comp = np.array([arp, [1, 0, 0], [0, 1, 0]])
a = comp.copy()
expected = np.ones(20)
for i in range(1, 20):
expected[i] = a[0, 0]
a = a.dot(comp)
assert_allclose(impulses, expected)
def test_har_forecast(self):
am = arch_model(self.har3, mean='HAR', vol='Constant', lags=[1, 5, 22])
res = am.fit()
fcast_1 = res.forecast(horizon=1)
fcast_5 = res.forecast(horizon=5)
assert_allclose(fcast_1.mean, fcast_5.mean.iloc[:, :1])
with pytest.raises(ValueError):
res.forecast(horizon=1, start=0)
with pytest.raises(ValueError):
res.forecast(horizon=1, start=20)
fcast_66 = res.forecast(horizon=66, start=21)
expected = np.empty((1000, 66 + 22))
expected.fill(np.nan)
for i in range(22):
if i < 21:
expected[21:, i] = self.har3.iloc[i:(-21 + i)]
else:
expected[21:, i] = self.har3.iloc[i:]
params = np.asarray(res.params)
const = params[0]
arp = np.zeros(22)
arp[0] = params[1]
arp[:5] += params[2] / 5
arp[:22] += params[3] / 22
arp_rev = arp[::-1]
for i in range(22, 88):
expected[:, i] = const + expected[:, i - 22:i].dot(arp_rev)
expected = expected[:, 22:]
assert_allclose(fcast_66.mean, expected)
expected[:22] = np.nan
expected[22:] = res.params.iloc[-1]
assert_allclose(fcast_66.residual_variance, expected)
impulse = _ar_to_impulse(66, arp)
expected = expected * np.cumsum(impulse**2)
assert_allclose(fcast_66.variance, expected)
def test_har_forecast(self):
am = arch_model(self.har3, mean='HAR', vol='Constant', lags=[1, 5, 22])
res = am.fit()
fcast_1 = res.forecast(horizon=1)
fcast_5 = res.forecast(horizon=5)
assert_allclose(fcast_1.mean, fcast_5.mean.iloc[:, :1])
with pytest.raises(ValueError):
res.forecast(horizon=1, start=0)
with pytest.raises(ValueError):
res.forecast(horizon=1, start=20)
fcast_66 = res.forecast(horizon=66, start=21)
expected = np.empty((1000, 66 + 22))
expected.fill(np.nan)
for i in range(22):
if i < 21:
expected[21:, i] = self.har3.iloc[i:(-21 + i)]
else:
expected[21:, i] = self.har3.iloc[i:]
params = np.asarray(res.params)
const = params[0]
arp = np.zeros(22)
arp[0] = params[1]
arp[:5] += params[2] / 5
arp[:22] += params[3] / 22
arp_rev = arp[::-1]
for i in range(22, 88):
expected[:, i] = const + expected[:, i - 22:i].dot(arp_rev)
expected = expected[:, 22:]
assert_allclose(fcast_66.mean, expected)
expected[:22] = np.nan
expected[22:] = res.params.iloc[-1]
assert_allclose(fcast_66.residual_variance, expected)
impulse = _ar_to_impulse(66, arp)
expected = expected * np.cumsum(impulse ** 2)
assert_allclose(fcast_66.variance, expected)
