analytic_filter function

analytic_filter

Fit a model given the observed value and the model parameters.

analytic_filter(
  outcomes,
  a1 = 0,
  R1 = 1,
  FF,
  FF.labs,
  G,
  G.labs,
  G.idx,
  D,
  h,
  H,
  p.monit = NA,
  monitoring = FALSE
)

Arguments

• outcomes: list: The observed data. It should contain objects of the class dlm_distr.
• a1: numeric: The prior mean at the latent vector.
• R1: matrix: The prior covariance matrix at the latent vector.
• FF: array: A 3D-array containing the planning matrix at each time. Its dimension should be n x k x t, where n is the number of latent states, k is the number of linear predictors in the model and t is the time series length.
• FF.labs: matrix: A character matrix containing the label associated with each value in FF.
• G: array: A 3D-array containing the evolution matrix at each time. Its dimension should be n x n x t, where n is the number of latent states and t is the time series length.
• G.labs: matrix: A character matrix containing the label associated with each value in G.
• G.idx: matrix: A numeric matrix containing the index associated with each value in G.
• D: array: A 3D-array containing the discount factor matrix at each time. Its dimension should be n x n x t, where n is the number of latent states and t is the time series length.
• h: matrix: A drift to be added after the temporal evolution (can be interpreted as the mean of the random noise at each time). Its dimension should be n x t, where t is the length of the series and n is the number of latent states.
• H: array: A 3D-array containing the covariance matrix of the noise at each time. Its dimension should be the same as D.
• p.monit: numeric (optional): The prior probability of changes in the latent space variables that are not part of its dynamic.
• monitoring: numeric: A vector of flags indicating which latent states should be monitored.

Returns

A list containing the following values:

• mt matrix: The filtered mean of the latent states for each time. Dimensions are n x t.
• Ct array: A 3D-array containing the filtered covariance matrix of the latent states for each time. Dimensions are n x n x t.
• at matrix: The one-step-ahead mean of the latent states at each time. Dimensions are n x t.
• Rt array: A 3D-array containing the one-step-ahead covariance matrix for latent states at each time. Dimensions are n x n x t.
• ft matrix: The one-step-ahead mean of the linear predictors at each time. Dimensions are k x t.
• Qt array: A 3D-array containing the one-step-ahead covariance matrix for linear predictors at each time. Dimensions are k x k x t.
• ft.star matrix: The filtered mean of the linear predictors for each time. Dimensions are k x t.
• Qt.star array: A 3D-array containing the linear predictors matrix of the latent state for each time. Dimensions are k x k x t.
• FF array: The same as the argument (same values).
• G matrix: The same as the argument (same values).
• G.labs matrix: The same as the argument (same values).
• G.idx matrix: The same as the argument (same values).
• D array: The same as the argument (same values).
• h array: The same as the argument (same values).
• H array: The same as the argument (same values).
• W array: A 3D-array containing the effective covariance matrix of the noise for each time, i.e., considering both H and D. Its dimension are the same as H and D.
• monitoring numeric: The same as the argument (same values).
• outcomes list: The same as the argument outcomes (same values).
• pred.names numeric: The names of the linear predictors.

Details

For the models covered in this package, we always use the approach described in \insertCite ArtigokParametrico;textualkDGLM, including, in particular, the filtering algorithm presented in that work.

For the details about the implementation see \insertCite ArtigoPacote;textualkDGLM.

For the details about the algorithm implemented see \insertCite ArtigokParametrico;textualkDGLM, \insertCite Petris-DLM;textualkDGLM, chapter 2, \insertCite WestHarr-DLM;textualkDGLM, chapter 4, and \insertCite Kalman_filter_origins;textualkDGLM.

References

\insertAllCited

See Also

fit_model

generic_smoother