Kfilter1 {astsa} | R Documentation |
Returns both the predicted and filtered values for a linear state space model. Also evaluates the likelihood at the given parameter values.
Kfilter1(num, y, A, mu0, Sigma0, Phi, Ups, Gam, cQ, cR, input)
num |
number of observations |
y |
data matrix, vector or time series |
A |
time-varying observation matrix, an array with |
mu0 |
initial state mean |
Sigma0 |
initial state covariance matrix |
Phi |
state transition matrix |
Ups |
state input matrix; use |
Gam |
observation input matrix; use |
cQ |
Cholesky-type decomposition of state error covariance matrix Q – see details below |
cR |
Cholesky-type decomposition of observation error covariance matrix R – see details below |
input |
matrix or vector of inputs having the same row dimension as y; use |
Practically, the script only requires that Q or R may be reconstructed as t(cQ)%*%(cQ)
or t(cR)%*%(cR)
, respectively.
xp |
one-step-ahead prediction of the state |
Pp |
mean square prediction error |
xf |
filter value of the state |
Pf |
mean square filter error |
like |
the negative of the log likelihood |
innov |
innovation series |
sig |
innovation covariances |
Kn |
last value of the gain, needed for smoothing |
D.S. Stoffer
http://www.stat.pitt.edu/stoffer/tsa4/
See also http://www.stat.pitt.edu/stoffer/tsa4/chap6.htm for an explanation of the difference between levels 0, 1, and 2.