Kfilter2 {astsa}R Documentation

Kalman Filter - Model may be time varying or have inputs or correlated errors

Description

Returns the filtered values for the state space model. In addition, the script returns the evaluation of the likelihood at the given parameter values and the innovation sequence.

Usage

Kfilter2(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 decomposition of state error covariance matrix Q – see details below

cR

Cholesky-type decomposition of observation error covariance matrix R – see details below

S

covariance-type 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

Details

cQ and cR are the Cholesky-type decompositions of Q and R. In particular, Q = t(cQ)%*%cQ and R = t(cR)%*%cR is all that is required (assuming Q and R are valid covariance matrices).

Value

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

innov

innovation series

sig

innovation covariances

K

last value of the gain, needed for smoothing

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts are https://www.stat.pitt.edu/stoffer/tsa4/ and https://www.stat.pitt.edu/stoffer/tsda/.


[Package astsa version 1.14 Index]