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astsa (version 1.4)

Kfilter0: Kalman Filter - Time Invariant Model

Description

Returns the filtered values in Property 6.1 on page 326 for the state-space model, (6.1) -- (6.2). In addition, returns the evaluation of the likelihood at the given parameter values and the innovation sequence. For demonstrations, see Example 6.5 on page 331,and Example 6.10 on page 350.

Usage

Kfilter0(num, y, A, mu0, Sigma0, Phi, cQ, cR)

Arguments

num
number of observations

y
data matrix, vector or time series

A
time-invariant observation matrix

mu0
initial state mean vector

Sigma0
initial state covariance matrix

Phi
state transition matrix

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

Value

xp
one-step-ahead state prediction
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

Details

Practically, the script only requires that Q or R may be reconstructed as t(cQ)%*%(cQ) or t(cR)%*%(cR), respectively.

References

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.