astsa (version 1.1)

Ksmooth2: Kalman Filter and Smoother - General model, may have correlated errors

Description

Returns the filtered and smoothed values in Property 6.5 on page 354 for the state-space model, (6.97) -- (6.99). This is the smoother companion to Kfilter2.

Usage

Ksmooth2(num, y, A, mu0, Sigma0, Phi, Ups, Gam, Theta, cQ, cR, 
          S, input)

Arguments

num

number of observations

y

data matrix, vector or time series

A

time-varying observation matrix, an array with dim=c(q,p,n)

mu0

initial state mean

Sigma0

initial state covariance matrix

Phi

state transition matrix

Ups

state input matrix; use Ups = 0 if not needed

Gam

observation input matrix; use Gam = 0 if not needed

Theta

state error pre-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

S

covariance matrix of state and observation errors

input

matrix or vector of inputs having the same row dimension as y; use input = 0 if not needed

Value

• xs
  state smoothers
• Ps
  smoother mean square error
• 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.