statespace_restrict

Filtering and smoothing under linear restrictions on the state (DK §6.6).

The restrictions \(R^*_t \alpha_t = r^*_t\) enter the observation equation as exact observations:

\[\begin{split}y^+_t = \begin{bmatrix} y_t \\ r^*_t \end{bmatrix}, \quad Z^+_t = \begin{bmatrix} Z_t \\ R^*_t \end{bmatrix}, \quad H^+_t = \begin{bmatrix} H_t & 0 \\ 0 & 0 \end{bmatrix}.\end{split}\]

A NaN in \(r^*_t\) leaves that restriction inactive in period t. The filtered and smoothed states satisfy the active restrictions exactly. The log likelihood of the result includes the restriction rows, so estimate parameters with the unrestricted model. Filter the result with FILTER_UNIVARIATE: once a restricted direction has no state noise, \(F_t\) is singular.

add_state_restrictions

subroutine add_state_restrictions(rep, Rmat, rval, rrep, info)
  type(ssm_rep_t), intent(in) :: rep
  real(dp), intent(in) :: Rmat(:, :, :)     ! (q, m, 1|n)  R*_t
  real(dp), intent(in) :: rval(:, :)        ! (q, n)       r*_t
  type(ssm_rep_t), intent(out) :: rrep
  integer, intent(out) :: info