SS                   package:dse1                   R Documentation

_S_t_a_t_e _S_p_a_c_e _M_o_d_e_l_s

_D_e_s_c_r_i_p_t_i_o_n:

     Construct a

_U_s_a_g_e:

         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)

_A_r_g_u_m_e_n_t_s:

      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.

_D_e_t_a_i_l_s:

     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.

_z_0 An initial value for z can be specified as z0.

_P_0 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. 

_V_a_l_u_e:

     An SS TSmodel

_S_e_e _A_l_s_o:

     `TSmodel' `ARMA'

_E_x_a_m_p_l_e_s:

         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)

