def _fit_no_arch_normal_errors(self,
cov_type: str = "robust"
) -> ARCHModelResult:
"""
Estimates model parameters
Parameters
----------
cov_type : str, optional
Covariance estimator to use when estimating parameter variances and
covariances. One of 'hetero' or 'heteroskedastic' for Whites's
covariance estimator, or 'mle' for the classic
OLS estimator appropriate for homoskedastic data. 'hetero' is the
the default.
Returns
-------
result : ARCHModelResult
Results class containing parameter estimates, estimated parameter
covariance and related estimates
Notes
-----
See :class:`ARCHModelResult` for details on computed results
"""
assert self._fit_y is not None
nobs = self._fit_y.shape[0]
if nobs < self.num_params:
raise ValueError("Insufficient data, " + str(self.num_params) +
" regressors, " + str(nobs) +
" data points available")
x = self._fit_regressors
y = self._fit_y
# Fake convergence results, see GH #87
opt = OptimizeResult({"status": 0, "message": ""})
if x.shape[1] > 0:
regression_params = np.linalg.pinv(x).dot(y)
xpxi = np.linalg.inv(x.T.dot(x) / nobs)
fitted = x.dot(regression_params)
else:
regression_params = np.empty(0)
xpxi = np.empty((0, 0))
fitted = 0.0
e = y - fitted
sigma2 = e.T.dot(e) / nobs
params = np.hstack((regression_params, sigma2))
hessian = np.zeros((self.num_params + 1, self.num_params + 1))
hessian[:self.num_params, :self.num_params] = -xpxi
hessian[-1, -1] = -1
if cov_type in ("mle", ):
param_cov = sigma2 * -hessian
param_cov[self.num_params, self.num_params] = 2 * sigma2**2.0
param_cov /= nobs
cov_type = COV_TYPES["classic_ols"]
elif cov_type in ("robust", ):
scores = np.zeros((nobs, self.num_params + 1))
scores[:, :self.num_params] = x * e[:, None]
scores[:, -1] = e**2.0 - sigma2
score_cov = scores.T.dot(scores) / nobs
param_cov = hessian.dot(score_cov).dot(hessian) / nobs
cov_type = COV_TYPES["white"]
else:
raise ValueError("Unknown cov_type")
r2 = self._r2(regression_params)
first_obs, last_obs = self._fit_indices
resids = np.empty_like(self._y, dtype=np.float64)
resids.fill(np.nan)
resids[first_obs:last_obs] = e
vol = np.zeros_like(resids)
vol.fill(np.nan)
vol[first_obs:last_obs] = np.sqrt(sigma2)
names = self._all_parameter_names()
loglikelihood = self._static_gaussian_loglikelihood(e)
# Throw away names in the case of starting values
num_params = params.shape[0]
if len(names) != num_params:
names = ["p" + str(i) for i in range(num_params)]
fit_start, fit_stop = self._fit_indices
return ARCHModelResult(
params,
param_cov,
r2,
resids,
vol,
cov_type,
self._y_series,
names,
loglikelihood,
self._is_pandas,
opt,
fit_start,
fit_stop,
copy.deepcopy(self),
)
def _fit_no_arch_normal_errors(self, cov_type='robust'):
"""
Estimates model parameters
Parameters
----------
cov_type : str, optional
Covariance estimator to use when estimating parameter variances and
covariances. One of 'hetero' or 'heteroskedastic' for Whites's
covariance estimator, or 'mle' for the classic
OLS estimator appropriate for homoskedastic data. 'hetero' is the
the default.
Returns
-------
result : ARCHModelResult
Results class containing parameter estimates, estimated parameter
covariance and related estimates
Notes
-----
See :class:`ARCHModelResult` for details on computed results
"""
nobs = self._fit_y.shape[0]
if nobs == 0:
from warnings import warn
warn('Cannot estimate model with no data', RuntimeWarning)
return None
if nobs < self.num_params:
raise ValueError('Insufficient data, ' + str(self.num_params) +
' regressors, ' + str(nobs) +
' data points available')
x = self._fit_regressors
y = self._fit_y
# Fake convergence results, see GH #87
opt = OptimizeResult({'status': 0, 'message': ''})
if x.shape[1] == 0:
loglikelihood = self._static_gaussian_loglikelihood(y)
names = self._all_parameter_names()
sigma2 = y.dot(y) / nobs
params = np.array([sigma2])
param_cov = np.array([[np.mean(y**2 - sigma2) / nobs]])
vol = np.zeros_like(y) * np.sqrt(sigma2)
# Throw away names in the case of starting values
num_params = params.shape[0]
if len(names) != num_params:
names = ['p' + str(i) for i in range(num_params)]
fit_start, fit_stop = self._fit_indices
return ARCHModelResult(params, param_cov, 0.0, y, vol, cov_type,
self._y_series, names, loglikelihood,
self._is_pandas, opt, fit_start, fit_stop,
copy.deepcopy(self))
regression_params = np.linalg.pinv(x).dot(y)
xpxi = np.linalg.inv(x.T.dot(x) / nobs)
e = y - x.dot(regression_params)
sigma2 = e.T.dot(e) / nobs
params = np.hstack((regression_params, sigma2))
hessian = np.zeros((self.num_params + 1, self.num_params + 1))
hessian[:self.num_params, :self.num_params] = -xpxi
hessian[-1, -1] = -1
if cov_type in ('mle', ):
param_cov = sigma2 * -hessian
param_cov[self.num_params, self.num_params] = 2 * sigma2**2.0
param_cov /= nobs
cov_type = COV_TYPES['classic_ols']
elif cov_type in ('robust', ):
scores = np.zeros((nobs, self.num_params + 1))
scores[:, :self.num_params] = x * e[:, None]
scores[:, -1] = e**2.0 - sigma2
score_cov = scores.T.dot(scores) / nobs
param_cov = hessian.dot(score_cov).dot(hessian) / nobs
cov_type = COV_TYPES['white']
else:
raise ValueError('Unknown cov_type')
r2 = self._r2(regression_params)
first_obs, last_obs = self._fit_indices
resids = np.empty_like(self._y, dtype=np.float64)
resids.fill(np.nan)
resids[first_obs:last_obs] = e
vol = np.zeros_like(resids)
vol.fill(np.nan)
vol[first_obs:last_obs] = np.sqrt(sigma2)
names = self._all_parameter_names()
loglikelihood = self._static_gaussian_loglikelihood(e)
# Throw away names in the case of starting values
num_params = params.shape[0]
if len(names) != num_params:
names = ['p' + str(i) for i in range(num_params)]
fit_start, fit_stop = self._fit_indices
return ARCHModelResult(params, param_cov, r2, resids, vol, cov_type,
self._y_series, names, loglikelihood,
self._is_pandas, opt, fit_start, fit_stop,
copy.deepcopy(self))