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

constrainedarray or list

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_variancearray

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

unconstrainedarray

Unconstrained parameters used by the optimizer, to be transformed to stationary coefficients of, e.g., an autoregressive or moving average component. Will match the type of the passed constrained variable (so if a list was passed, a list will be returned).

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.