, transformed=True, includes_fixed=False, cov_type='none', cov_kwds=None, method='em', maxiter=500, tolerance=1e-06, em_initialization=True, mstep_method=None, full_output=1, disp=False, callback=None, return_params=False, optim_score=None, optim_complex_step=None, optim_hessian=None, flags=None, low_memory=False, llf_decrease_action='revert', llf_decrease_tolerance=0.0001, **kwargs)[source]

Fits the model by maximum likelihood via Kalman filter.

start_paramsarray_like, optional

Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params.

transformedbool, optional

Whether or not start_params is already transformed. Default is True.

includes_fixedbool, optional

If parameters were previously fixed with the fix_params method, this argument describes whether or not start_params also includes the fixed parameters, in addition to the free parameters. Default is False.

cov_typestr, optional

The cov_type keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of:

  • ‘opg’ for the outer product of gradient estimator

  • ‘oim’ for the observed information matrix estimator, calculated using the method of Harvey (1989)

  • ‘approx’ for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix.

  • ‘robust’ for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the ‘oim’ method.

  • ‘robust_approx’ is the same as ‘robust’ except that the intermediate calculations use the ‘approx’ method.

  • ‘none’ for no covariance matrix calculation.

Default is ‘none’, since computing this matrix can be very slow when there are a large number of parameters.

cov_kwdsdict or None, optional

A dictionary of arguments affecting covariance matrix computation.

opg, oim, approx, robust, robust_approx

  • ‘approx_complex_step’ : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True.

  • ‘approx_centered’ : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False.

methodstr, optional

The method determines which solver from scipy.optimize is used, and it can be chosen from among the following strings:

  • ‘em’ for the EM algorithm

  • ‘newton’ for Newton-Raphson

  • ‘nm’ for Nelder-Mead

  • ‘bfgs’ for Broyden-Fletcher-Goldfarb-Shanno (BFGS)

  • ‘lbfgs’ for limited-memory BFGS with optional box constraints

  • ‘powell’ for modified Powell’s method

  • ‘cg’ for conjugate gradient

  • ‘ncg’ for Newton-conjugate gradient

  • ‘basinhopping’ for global basin-hopping solver

The explicit arguments in fit are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports.

maxiterint, optional

The maximum number of iterations to perform.

tolerancefloat, optional

Tolerance to use for convergence checking when using the EM algorithm. To set the tolerance for other methods, pass the optimizer-specific keyword argument(s).

full_outputbool, optional

Set to True to have all available output in the Results object’s mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information.

dispbool, optional

Set to True to print convergence messages.

callbackcallable callback(xk), optional

Called after each iteration, as callback(xk), where xk is the current parameter vector.

return_paramsbool, optional

Whether or not to return only the array of maximizing parameters. Default is False.

optim_score{‘harvey’, ‘approx’} or None, optional

The method by which the score vector is calculated. ‘harvey’ uses the method from Harvey (1989), ‘approx’ uses either finite difference or complex step differentiation depending upon the value of optim_complex_step, and None uses the built-in gradient approximation of the optimizer. Default is None. This keyword is only relevant if the optimization method uses the score.

optim_complex_stepbool, optional

Whether or not to use complex step differentiation when approximating the score; if False, finite difference approximation is used. Default is True. This keyword is only relevant if optim_score is set to ‘harvey’ or ‘approx’.

optim_hessian{‘opg’,’oim’,’approx’}, optional

The method by which the Hessian is numerically approximated. ‘opg’ uses outer product of gradients, ‘oim’ uses the information matrix formula from Harvey (1989), and ‘approx’ uses numerical approximation. This keyword is only relevant if the optimization method uses the Hessian matrix.

low_memorybool, optional

If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Note that this option is not available when using the EM algorithm (which is the default for this model). Default is False.

llf_decrease_action{‘ignore’, ‘warn’, ‘revert’}, optional

Action to take if the log-likelihood decreases in an EM iteration. ‘ignore’ continues the iterations, ‘warn’ issues a warning but continues the iterations, while ‘revert’ ends the iterations and returns the result from the last good iteration. Default is ‘warn’.

llf_decrease_tolerancefloat, optional

Minimum size of the log-likelihood decrease required to trigger a warning or to end the EM iterations. Setting this value slightly larger than zero allows small decreases in the log-likelihood that may be caused by numerical issues. If set to zero, then any decrease will trigger the llf_decrease_action. Default is 1e-4.


Additional keyword arguments to pass to the optimizer.


Last update: May 14, 2024