SS: 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.nonInnov.SS(obj)

Arguments

(nxn) is the state transition matrix F.

(pxn)is the output matrix H.

(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.

(pxp) is the input matrix of the output (measurement) noise, which is assumed white. (probably need R if p>n )

(nxp)is the control (input) matrix. G should be NULL if there is no input.

(nxp)is the Kalman gain.

vector indicating estimate of the state at time 0. Set to zero if not supplied.

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.

Value

An SS TSmodel

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. }

Examples

Run this code

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)