Description

transformSSM transforms the general multivariate Gaussian state space model to form suitable for sequential processing.

Usage

Arguments

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.

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