astsa (version 1.1)

Ksmooth1: Kalman Filter and Smoother - General model

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, (6.3) -- (6.4). For demonstrations, see Example 6.7 on page 338 and Example 6.9 on page 348.

Usage

Ksmooth1(num, y, A, mu0, Sigma0, Phi, Ups, Gam, cQ, cR, 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

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

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
• 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.