statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothing.observed_information_matrix¶

ExponentialSmoothing.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.

**kwargs

Additional keyword arguments to pass to the Kalman filter. See KalmanFilter.filter for more details.

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.