astsa (version 1.1)

Ksmooth0: Kalman Filter and Smoother - Time invariant model without inputs

Description

Returns both the filtered values in Property 6.1 on page 326 and the smoothed values in Property 6.2 on page 330 for the state-space model, (6.1) -- (6.2). For demonstrations, see Example 6.5 on page 331, and Example 6.10 on page 350.

Usage

Ksmooth0(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

• xs
  state smoothers
• Ps
  smoother mean square error
• x0n
  initial mean smoother
• P0n
  initial smoother covariance
• J0
  initial value of the J matrix
• J
  the J matrices
• 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
• Kn
  last value of the gain

Details

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.

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.