astsa (version 1.1)

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 state 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/tsa3/ See also http://www.stat.pitt.edu/stoffer/tsa3/chap6.htm for an explanation of the difference between levels 0, 1, and 2.