statsmodels.tsa.statespace.tools.unconstrain_stationary_multivariate

statsmodels.tsa.statespace.tools.unconstrain_stationary_multivariate(constrained, error_variance)

Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer

Parameters:

constrainedndarray or list of ndarray

Constrained parameters of, e.g., an autoregressive or moving average component, to be transformed to arbitrary parameters used by the optimizer. If a list, should be a list of length order, where each element is an array sized k_endog x k_endog. If an array, should be the coefficient matrices horizontally concatenated and sized k_endog x k_endog * order.

error_variancendarray

The variance / covariance matrix of the error term. Should be sized k_endog x k_endog. This is used as input in the algorithm even if is not transformed by it (when transform_variance is False).

Returns:

unconstrainedndarray or list of ndarray

Unconstrained parameters used by the optimizer. Will match the type of the passed constrained variable (so if a list was passed, a list will be returned).

error_variancendarray

The variance / covariance matrix of the error term. This is the same as the input error_variance, since this function does not transform the error variance term.

Notes

Uses the list representation internally, even if an array is passed.

References

[*]

Ansley, Craig F., and Robert Kohn. 1986. “A Note on Reparameterizing a Vector Autoregressive Moving Average Model to Enforce Stationarity.” Journal of Statistical Computation and Simulation 24 (2): 99-106.