R: Transform Multivariate State Space Model for Sequential...
transformSSM
R Documentation
Transform Multivariate State Space Model for Sequential Processing
Description
transformSSM transforms the general multivariate Gaussian state space model
to form suitable for sequential processing.
Usage
transformSSM(object, type = c("ldl", "augment"))
Arguments
object
State space model object from function SSModel.
type
Option "ldl" performs LDL decomposition for covariance matrix H[t],
and multiplies the observation equation with the L[t]^-1, so ε[t]* ~ N(0,D[t]). Option "augment" adds
ε[t] to the state vector, so Q[t] becomes block diagonal
with blocks Q[t] and H[t].
Details
As all the functions in KFAS use univariate approach i.e. sequential processing,
the covariance matrix H[t] of the observation equation needs to be
either diagonal or zero matrix. Function transformSSM performs either
the LDL decomposition of H[t], or augments the state vector with
the disturbances of the observation equation.
In case of a LDL decomposition, the new H[t] contains the diagonal part of the
decomposition, whereas observations y[t] and system matrices Z[t] are
multiplied with the inverse of L[t]. Note that although the state estimates and
their error covariances obtained by Kalman filtering and smoothing are identical with those
obtained from ordinary multivariate filtering, the one-step-ahead errors
v[t] and their variances F[t] do differ. The typical
multivariate versions can be obtained from output of KFS
using mvInnovations function.
providing 
.