transformSSM {KFAS}

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"), tol)

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 \epsilon_t^* \sim N(0,D_t). Option "augment" adds \epsilon_t to the state vector, so Q_t becomes block diagonal with blocks Q_t and H_t.

tol

Tolerance parameter for LDL decomposition (see ldl). Default is max(100, max(abs(apply(object$H, 3, diag)))) * .Machine$double.eps.

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.

In case of augmentation of the state vector, some care is needed interpreting the subsequent filtering/smoothing results: For example the muhat from the output of KFS now contains also the smoothed observational level noise as that is part of the state vector.

Value

model

Transformed model.