def fit_cor(copula, data: np.ndarray, typ: str) -> np.ndarray:
"""
Constructs parameter matrix from matrix of Kendall's Taus or Spearman's Rho
Parameters
----------
copula: BaseCopula
Copula instance
data: ndarray
Data to fit copula with
typ: {'irho', 'itau'}
The type of rank correlation measure to use. 'itau' uses Kendall's tau while 'irho' uses Spearman's rho
Returns
-------
ndarray
Parameter matrix is copula is elliptical. Otherwise, a vector
"""
indices = tri_indices(copula.dim, 1, 'lower')
if typ == 'itau':
tau = kendall_tau(data)[indices]
theta = copula.itau(tau)
elif typ == 'irho':
rho = spearman_rho(data)[indices]
theta = copula.irho(rho)
else:
raise ValueError(
"Correlation Inversion must be either 'itau' or 'irho'")
if is_elliptical(copula):
theta = near_psd(create_cov_matrix(theta))[indices]
return theta
def initial_params(self) -> np.ndarray:
if self.x0 is not None:
return self.x0
if is_elliptical(self.copula):
corr = pearson_rho(self.data)
rhos = corr[tri_indices(self.copula.dim, 1, 'lower')]
if hasattr(self.copula, '_df'):
# T-distribution
return np.array([4.669,
*rhos]) # set df as Feigenbaum's constant
else:
# Gaussian
return rhos
try:
start = CorrInversionEstimator(self.copula, self.data,
self.verbose).fit('itau')
ll = self.copula.log_lik(self.data)
if np.isfinite(ll):
return start
else:
if self.copula.name.lower(
) == 'clayton' and self.copula.dim == 2:
# The support of bivariate claytonCopula with negative parameter is not
# the full unit square; the further from 0, the more restricted.
while start < 0:
start += .2
self.copula.params = start
if np.isfinite(self.copula.log_lik(self.data)):
break
if not np.isnan(ll) and np.isinf(ll):
# for perfectly correlated data
return start
return self.copula.params
except NotImplementedError:
return self.copula.params
def initial_params(copula: Copula, data: np.ndarray, x0: np.ndarray):
# ensure that initial is defined. If it is defined, checks that all x0 values are finite
# neither infinite nor nan
if x0 is not None and \
((np.isscalar(x0) and not np.isfinite(x0)) or (not np.isscalar(x0) and all(np.isfinite(x0)))):
return x0
if is_elliptical(copula):
corr = pearson_rho(data)
rhos = corr[tri_indices(copula.dim, 1, 'lower')]
if copula.name.lower() == 'student':
# T-distribution
return np.array([4.669, *rhos]) # set df as Feigenbaum's constant
else:
# Gaussian
return rhos
try:
start = estimate_corr_inverse_params(copula, data, 'itau')
ll = copula.log_lik(data)
if np.isfinite(ll):
return start
else:
if copula.name.lower() == 'clayton' and copula.dim == 2:
# The support of bivariate claytonCopula with negative parameter is not
# the full unit square; the further from 0, the more restricted.
while start < 0:
start += .2
copula.params = start
if np.isfinite(copula.log_lik(data)):
break
if not np.isnan(ll) and np.isinf(ll):
# for perfectly correlated data
return start
return copula.params
except NotImplementedError:
return copula.params
def estimate_corr_inverse_params(copula, data: np.ndarray,
type_: Literal['itau', 'irho']):
"""
Fits the copula with the inversion of Spearman's rho or Kendall's tau Estimator
Parameters
----------
copula
Copula whose parameters are to be estimated
data
Data to fit the copula with
type_ : {'irho', 'itau'}
The type of rank correlation measure to use. 'itau' uses Kendall's tau while 'irho' uses Spearman's rho
"""
type_ = type_.lower()
if type_ not in ('itau', 'irho'):
raise ValueError(
"Correlation Inversion must be either 'itau' or 'irho'")
icor = fit_cor(copula, data, type_)
if is_elliptical(copula):
estimate = icor
copula.params[:] = estimate
elif is_archimedean(copula):
estimate = np.mean(icor)
copula.params = estimate
else:
raise NotImplementedError(
f"Have not developed for '{copula.name} copula'")
method = f"Inversion of {'Spearman Rho' if type_ == 'irho' else 'Kendall Tau'} Correlation"
copula.fit_smry = FitSummary(estimate, method, copula.log_lik(data),
len(data))
return estimate
def fit(self, typ: str) -> np.ndarray:
"""
Fits the copula with the inversion of Spearman's rho or Kendall's tau Estimator
Parameters
----------
typ: {'irho', 'itau'}
The type of rank correlation measure to use. 'itau' uses Kendall's tau while 'irho' uses Spearman's rho
Returns
-------
ndarray
Estimates for the copula
"""
typ = typ.lower()
if typ not in ('itau', 'irho'):
raise ValueError(
"Correlation Inversion must be either 'itau' or 'irho'")
icor = fit_cor(self.copula, self.data, typ)
if is_elliptical(self.copula):
estimate = icor
self.copula.params[:] = estimate
elif is_archimedean(self.copula):
estimate = np.mean(icor)
self.copula.params = estimate
else:
raise NotImplementedError(
f"Have not developed for '{self.copula.name} copula'")
method = f"Inversion of {'Spearman Rho' if typ == 'irho' else 'Kendall Tau'} Correlation"
self.copula.fit_smry = FitSummary(estimate, method,
self.copula.log_lik(self.data),
len(self.data))
return estimate