Returns both the filtered and the smoothed values for the state-space model.
Ksmooth1(num, y, A, mu0, Sigma0, Phi, Ups, Gam, cQ, cR, input)number of observations
data matrix, vector or time series
time-varying observation matrix, an array with dim=c(q,p,n)
initial state mean
initial state covariance matrix
state transition matrix
state input matrix; use Ups = 0 if not needed
observation input matrix; use Gam = 0 if not needed
Cholesky-type decomposition of state error covariance matrix Q -- see details below
Cholesky-type decomposition of observation error covariance matrix R -- see details below
matrix or vector of inputs having the same row dimension as y; use input = 0 if not needed
state smoothers
smoother mean square error
initial mean smoother
initial smoother covariance
initial value of the J matrix
the J matrices
one-step-ahead prediction of the state
mean square prediction error
filter value of the state
mean square filter error
the negative of the log likelihood
last value of the gain
Practically, the script only requires that Q or R may be reconstructed as
t(cQ)%*%(cQ) or t(cR)%*%(cR), respectively, which allows more flexibility.
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.