SS {dse1}R Documentation

State Space Models

Description

Construct a

Usage

    SS(F.=NULL, G=NULL, H=NULL, K=NULL, Q=NULL, R=NULL, z0=NULL, P0=NULL,
             description=NULL, names=NULL, input.names=NULL, output.names=NULL)
    is.SS(obj)
    is.innov.SS(obj)
    is.non.innov.SS(obj)

Arguments

F. (nxn) is the state transition matrix F.
H (pxn)is the output matrix H.
Q (nxn) is the input matrix of the system noise and the noise is assumed to be white. Some authors (eg. Harvey) modify this as rt*qt*rt' where rt is the matrix for the system noise and qt is the noise cov, but that is redundant.
R (pxp) is the input matrix of the output (measurement) noise, which is assumed white. (probably need R if p>n )
G (nxp)is the control (input) matrix. G should be NULL if there is no input.
K (nxp)is the Kalman gain.
z0 vector indicating estimate of the state at time 0. Set to zero if not supplied.
P0 a matrix indicating initial tracking error P(t=1|t=0). Set to I if not supplied.
description String. An arbitrary description.
names A list with elements input and output, each a vector of strings. Arguments input.names and output.names should not be used if argument names is used.
input.names A vector of character strings indicating input variable names.
output.names A vector of character strings indicating output variable names.
obj an object.

Details

State space models have a further sub-class: innov or non-innov, indicating an innovations form or a non-innovations form.

The state space (SS) model is defined by:

z(t) = Fz(t-1) + Gu(t) + Qe(t) y(t) = Hz(t) + Rw(t)

or the innovations model:

z(t) = Fz(t-1) + Gu(t) + Kw(t-1) y(t) = Hz(t) + w(t)

F
(nxn) is the state transition matrix F.
H
(pxn)is the output matrix H.
Q
(nxn) is the input matrix of the system noise and the noise is assumed to be white. Some authors (eg. Harvey) modify this as rt*qt*rt' where rt is the matrix for the system noise and qt is the noise cov, but that is redundant.
R
(pxp) is the input matrix of the output (measurement) noise, which is assumed white. (probably need R if p>n )
G
(nxp)is the control (input) matrix.
K
(nxp)is the Kalman gain.
y
is the p dimensional output data.
u
is the m dimensional exogenous (input) data.
z
is the n dimensional (estimated) state at time t, E[z(t)|y(t-1), u(t)] denoted E[z(t)|t-1]. An initial value for z can be specified as z0 and an initial one step ahead state tracking error (for non-innovations models) as P0.
z0
An initial value for z can be specified as z0.
P0
An initial one step ahead state tracking error (for non-innovations models) can be specified as P0.
K, Q, R
For sub-class innov the Kalman gain K is specified but not Q and R. For sub-class non-innov Q and R are specified but not the Kalman gain K.

Value

An SS TSmodel

See Also

TSmodel ARMA

Examples

    f <- array(c(.5,.3,.2,.4),c(2,2))
    h <- array(c(1,0,0,1),c(2,2))
    k <- array(c(.5,.3,.2,.4),c(2,2))
    ss <- SS(F=f,G=NULL,H=h,K=k)
    is.SS(ss)
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