Ksmooth2 {astsa}R Documentation

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

Description

Returns the filtered and smoothed values for the state-space model. 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 observation 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

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

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

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]