Gaussian¶

The implementation of the Gaussian (Normal) copula is such that all the univariate marginal distributions are normal and the multivariate joint distribution is a multivariate-normal distribution.

class copulae.elliptical.GaussianCopula(*args, **kwds)[source]¶

The Gaussian (Normal) copula. It is elliptical and symmetric which gives it nice analytical properties. The Gaussian copula is determined entirely by its correlation matrix.

Gaussian copulas do not model tail dependencies very well, it’s tail is flat. Take not that by symmetry, it gives equal weight to tail scenarios. In English, this means upside scenarios happen as often as downside scenarios.

A Gaussian copula is fined as

\[C_\Sigma (u_1, \dots, u_d) = \Phi_\Sigma (N^{-1} (u_1), \dots, N^{-1} (u_d))\]

where \(\Sigma\) is the covariance matrix which is the parameter of the Gaussian copula and \(N^{-1}\) is the quantile (inverse cdf) function

property bounds¶

Gets the bounds for the parameters

Returns: Lower and upper bound of the copula’s parameters
Return type: (scalar or array_like, scalar or array_like)

property dim¶: Number of dimensions in copula

fit(data, x0=None, method='ml', optim_options=None, ties='average', verbose=1, to_pobs=True, scale=1.0)¶

Fit the copula with specified data

Parameters

data (ndarray) – Array of data used to fit copula. Usually, data should be the pseudo observations
x0 (ndarray) – Initial starting point. If value is None, best starting point will be estimated
method ({ 'ml', 'irho', 'itau' }, optional) – Method of fitting. Supported methods are: ‘ml’ - Maximum Likelihood, ‘irho’ - Inverse Spearman Rho, ‘itau’ - Inverse Kendall Tau
optim_options (dict, optional) – Keyword arguments to pass into scipy.optimize.minimize()
ties ({ 'average', 'min', 'max', 'dense', 'ordinal' }, optional) – Specifies how ranks should be computed if there are ties in any of the coordinate samples. This is effective only if the data has not been converted to its pseudo observations form
verbose (int, optional) – Log level for the estimator. The higher the number, the more verbose it is. 0 prints nothing.
to_pobs (bool) – If True, casts the input data along the column axis to uniform marginals (i.e. convert variables to values between [0, 1]). Set this to False if the input data are already uniform marginals.
scale (float) – Amount to scale the objective function value of the numerical optimizer. This is helpful in achieving higher accuracy as it increases the sensitivity of the optimizer. The downside is that the optimizer could likely run longer as a result. Defaults to 1.