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.nonInnov.SS(obj)

### Arguments

`F.` | (nxn) state transition matrix.
`H` | (pxn) output matrix.
`Q` | (nxn) matrix specifying the system noise distribution.
`R` | (pxp) matrix specifying the output (measurement) noise distribution.
`G` | (nxp) input (control) matrix. G should be NULL if there is no input.
`K` | (nxp) matrix specifying the Kalman gain.
`z0` | vector indicating estimate of the state at time 0. Set to zero if not supplied.
`P0` | 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)

Matrices are as specified above in the aguments, and

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.
e and w
  are typically assumed to be white noise in the non-innovations form, in which case the covariance of the system noise is QQ' and the covariance of the measurement noise is RR'. The covariance of e and w can be specified otherwise in the simulate method `simulate.SS` for this class of model, but the assumption is usually maintained when estimating models of this form (although, not by all authors).

  Typically, an non-innovations form is harder to identify than an innovations form. Non-innovations form would typically be choosen when there is considerable theoretical or physical knowledge of the system (e.g. the system was built from known components with measured physical values).

  By default, elements in parameter matrices are treated as constants if they are exactly 1.0 or 0.0, and as parameters otherwise. A value of 1.001 would be treated as a parameter, and this is the easiest way to initialize an element which is not to be treated as a constant of value 1.0. Any matrix elements can be fixed to constants of any value using fixConstants.

### Value

An SS TSmodel

### See Also

`TSmodel` `ARMA` `simulate.SS` `l.SS` `fixConstants`

### 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)
        ss

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