def test_ar1_forecast_simulation(self):
am = arch_model(self.ar1, mean="AR", vol="GARCH", lags=[1])
res = am.fit(disp="off")
with preserved_state(self.rng):
forecast = res.forecast(horizon=5, start=0, method="simulation")
y = np.asarray(self.ar1)
index = self.ar1.index
t = y.shape[0]
params = np.array(res.params)
resids = np.asarray(y[1:] - params[0] - params[1] * y[:-1])
vol = am.volatility
params = np.array(res.params)
backcast = vol.backcast(resids)
var_bounds = vol.variance_bounds(resids)
rng = am.distribution.simulate([])
vfcast = vol.forecast(
params[2:],
resids,
backcast,
var_bounds,
start=0,
method="simulation",
rng=rng,
horizon=5,
)
const, ar = params[0], params[1]
means = np.zeros((t, 5))
means[:, 0] = const + ar * y
for i in range(1, 5):
means[:, i] = const + ar * means[:, i - 1]
means = pd.DataFrame(means,
index=index,
columns=["h.{0}".format(j) for j in range(1, 6)])
assert_frame_equal(means, forecast.mean)
var = np.concatenate([[[np.nan] * 5], vfcast.forecasts])
rv = pd.DataFrame(var,
index=index,
columns=["h.{0}".format(j) for j in range(1, 6)])
assert_frame_equal(rv, forecast.residual_variance)
lrv = rv.copy()
for i in range(5):
weights = (ar**np.arange(i + 1))**2
weights = weights[:, None]
lrv.iloc[:, i:i + 1] = rv.values[:, :i + 1].dot(weights[::-1])
assert_frame_equal(lrv, forecast.variance)
def test_ar1_forecast_simulation(self):
am = arch_model(self.ar1, mean='AR', vol='GARCH', lags=[1])
res = am.fit(disp='off')
with preserved_state(self.rng):
forecast = res.forecast(horizon=5, start=0, method='simulation')
y = np.asarray(self.ar1)
index = self.ar1.index
t = y.shape[0]
params = np.array(res.params)
resids = np.asarray(y[1:] - params[0] - params[1] * y[:-1])
vol = am.volatility
params = np.array(res.params)
backcast = vol.backcast(resids)
var_bounds = vol.variance_bounds(resids)
rng = am.distribution.simulate([])
vfcast = vol.forecast(params[2:], resids, backcast, var_bounds, start=0,
method='simulation', rng=rng, horizon=5)
const, ar = params[0], params[1]
means = np.zeros((t, 5))
means[:, 0] = const + ar * y
for i in range(1, 5):
means[:, i] = const + ar * means[:, i - 1]
means = pd.DataFrame(means, index=index,
columns=['h.{0}'.format(j) for j in range(1, 6)])
assert_frame_equal(means, forecast.mean)
var = np.concatenate([[[np.nan] * 5], vfcast.forecasts])
rv = pd.DataFrame(var, index=index,
columns=['h.{0}'.format(j) for j in range(1, 6)])
assert_frame_equal(rv, forecast.residual_variance)
lrv = rv.copy()
for i in range(5):
weights = (ar ** np.arange(i + 1)) ** 2
weights = weights[:, None]
lrv.iloc[:, i:i + 1] = rv.values[:, :i + 1].dot(weights[::-1])
assert_frame_equal(lrv, forecast.variance)
