def forecast(
self,
params: ArrayLike1D,
horizon: int = 1,
start: Optional[Union[int, DateLike]] = None,
align: str = "origin",
method: str = "analytic",
simulations: int = 1000,
rng: Optional[Callable[[Union[int, Tuple[int, ...]]], NDArray]] = None,
random_state: Optional[np.random.RandomState] = None,
) -> ARCHModelForecast:
# Check start
earliest, default_start = self._fit_indices
default_start = max(0, default_start - 1)
start_index = cutoff_to_index(start, self._y_series.index,
default_start)
if start_index < (earliest - 1):
raise ValueError(
"Due to backcasting and/or data availability start cannot be less "
"than the index of the largest value in the right-hand-side "
"variables used to fit the first observation. In this model, "
"this value is {0}.".format(max(0, earliest - 1)))
# Parse params
params = np.asarray(params)
mp, vp, dp = self._parse_parameters(params)
#####################################
# Compute residual variance forecasts
#####################################
# Back cast should use only the sample used in fitting
resids = self.resids(mp)
backcast = self._volatility.backcast(resids)
full_resids = self.resids(mp, self._y[earliest:],
self.regressors[earliest:])
vb = self._volatility.variance_bounds(full_resids, 2.0)
if rng is None:
rng = self._distribution.simulate(dp)
variance_start = max(0, start_index - earliest)
vfcast = self._volatility.forecast(
vp,
full_resids,
backcast,
vb,
start=variance_start,
horizon=horizon,
method=method,
simulations=simulations,
rng=rng,
random_state=random_state,
)
var_fcasts = vfcast.forecasts
var_fcasts = _forecast_pad(earliest, var_fcasts)
arp = self._har_to_ar(mp)
nexog = 0 if self._x is None else self._x.shape[1]
exog_p = np.empty([]) if self._x is None else mp[-nexog:]
constant = arp[0] if self.constant else 0.0
dynp = arp[int(self.constant):]
mean_fcast = _ar_forecast(self._y, horizon, start_index, constant,
dynp, exog_p, self._x)
# Compute total variance forecasts, which depend on model
impulse = _ar_to_impulse(horizon, dynp)
longrun_var_fcasts = var_fcasts.copy()
for i in range(horizon):
lrf = var_fcasts[:, :(i + 1)].dot(impulse[i::-1]**2)
longrun_var_fcasts[:, i] = lrf
if method.lower() in ("simulation", "bootstrap"):
# TODO: This is not tested, but probably right
variance_paths = _forecast_pad(earliest, vfcast.forecast_paths)
long_run_variance_paths = variance_paths.copy()
shocks = _forecast_pad(earliest, vfcast.shocks)
for i in range(horizon):
_impulses = impulse[i::-1][:, None]
lrvp = variance_paths[start_index:, :, :(i + 1)].dot(
_impulses**2)
long_run_variance_paths[start_index:, :, i] = np.squeeze(lrvp)
t, m = self._y.shape[0], self._max_lags
mean_paths = np.full((t, simulations, m + horizon), np.nan)
dynp_rev = dynp[::-1]
for i in range(start_index, t):
mean_paths[i, :, :m] = self._y[i - m + 1:i + 1]
for j in range(horizon):
mean_paths[i, :, m +
j] = (constant +
mean_paths[i, :, j:m + j].dot(dynp_rev) +
shocks[i, :, j])
mean_paths = mean_paths[:, :, m:]
else:
variance_paths = mean_paths = shocks = long_run_variance_paths = None
index = self._y_series.index
return ARCHModelForecast(
index,
mean_fcast,
longrun_var_fcasts,
var_fcasts,
align=align,
simulated_paths=mean_paths,
simulated_residuals=shocks,
simulated_variances=long_run_variance_paths,
simulated_residual_variances=variance_paths,
)
def forecast(self,
parameters,
horizon=1,
start=None,
align='origin',
method='analytic',
simulations=1000):
# Check start
earliest, default_start = self._fit_indices
default_start = max(0, default_start - 1)
start_index = cutoff_to_index(start, self._y_series.index,
default_start)
if start_index < (earliest - 1):
raise ValueError(
'Due ot backcasting and/or data availability start cannot be less '
'than the index of the largest value in the right-hand-side '
'variables used to fit the first observation. In this model, '
'this value is {0}.'.format(max(0, earliest - 1)))
# Parse params
parameters = np.asarray(parameters)
mp, vp, dp = self._parse_parameters(parameters)
#####################################
# Compute residual variance forecasts
#####################################
# Back cast should use only the sample used in fitting
resids = self.resids(mp)
backcast = self._volatility.backcast(resids)
full_resids = self.resids(mp, self._y[earliest:],
self.regressors[earliest:])
vb = self._volatility.variance_bounds(full_resids, 2.0)
rng = self._distribution.simulate(dp)
variance_start = max(0, start_index - earliest)
vfcast = self._volatility.forecast(vp,
full_resids,
backcast,
vb,
start=variance_start,
horizon=horizon,
method=method,
simulations=simulations,
rng=rng)
var_fcasts = vfcast.forecasts
var_fcasts = _forecast_pad(earliest, var_fcasts)
arp = self._har_to_ar(mp)
nexog = 0 if self._x is None else self._x.shape[1]
exog_p = np.empty([]) if self._x is None else mp[-nexog:]
constant = arp[0] if self.constant else 0.0
dynp = arp[int(self.constant):]
mean_fcast = _ar_forecast(self._y, horizon, start_index, constant,
dynp, exog_p, self._x)
# Compute total variance forecasts, which depend on model
impulse = _ar_to_impulse(horizon, dynp)
longrun_var_fcasts = var_fcasts.copy()
for i in range(horizon):
lrf = var_fcasts[:, :(i + 1)].dot(impulse[i::-1]**2)
longrun_var_fcasts[:, i] = lrf
if method.lower() in ('simulation', 'bootstrap'):
# TODO: This is not tested, and probably wrong
variance_paths = _forecast_pad(earliest, vfcast.forecast_paths)
long_run_variance_paths = variance_paths.copy()
shocks = _forecast_pad(earliest, vfcast.shocks)
for i in range(horizon):
_impulses = impulse[i::-1][:, None]
lrvp = variance_paths[:, :, :(i + 1)].dot(_impulses**2)
long_run_variance_paths[:, :, i] = np.squeeze(lrvp)
t, m = self._y.shape[0], self._max_lags
mean_paths = np.empty((t, simulations, m + horizon))
mean_paths.fill(np.nan)
dynp_rev = dynp[::-1]
for i in range(start_index, t):
mean_paths[i, :, :m] = self._y[i - m + 1:i + 1]
for j in range(horizon):
mean_paths[i, :, m + j] = constant + \
mean_paths[i, :, j:m + j].dot(dynp_rev) + \
shocks[i, :, j]
mean_paths = mean_paths[:, :, m:]
else:
variance_paths = mean_paths = shocks = long_run_variance_paths = None
index = self._y_series.index
return ARCHModelForecast(index,
mean_fcast,
longrun_var_fcasts,
var_fcasts,
align=align,
simulated_paths=mean_paths,
simulated_residuals=shocks,
simulated_variances=long_run_variance_paths,
simulated_residual_variances=variance_paths)