statsmodels.tsa.statespace.dynamic_factor_mq.DynamicFactorMQ.observed_information_matrix#
- DynamicFactorMQ.observed_information_matrix(params, transformed=True, includes_fixed=False, approx_complex_step=None, approx_centered=False, **kwargs)#
Observed information matrix
- Parameters:
- paramsarray_like,
optional Array of parameters at which to evaluate the loglikelihood function.
- transformedbool,
optional Whether or not 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 params also includes the fixed parameters, in addition to the free parameters. Default is False.
- approx_complex_stepbool,
optional Whether or not to approximate the derivatives of the loglikelihood using complex step differentiation. Default is True if transformed is True.
- approx_centeredbool,
optional Whether or not to use a centered approximation for finite difference derivatives, when approx_complex_step is False. Default is False.
- **kwargs
Additional keyword arguments to pass to the Kalman filter. See KalmanFilter.filter for more details.
- paramsarray_like,
Notes
This method is from Harvey (1989), which shows that the information matrix only depends on terms from the gradient. This implementation is partially analytic and partially numeric approximation, therefore, because it uses the analytic formula for the information matrix, with numerically computed elements of the gradient.
References
Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.