transformSSM {KFAS}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.

Value

model

Transformed model.


[Package KFAS version 1.3.7 Index]