arsimul

armax simulation

Calling Sequence

[z]=arsimul(a,b,d,sig,u,[up,yp,ep])
[z]=arsimul(ar,u,[up,yp,ep])

Arguments

:ar an armax process. See armac. : :a is the matrix [Id,a1,...,a_r] of dimension (n,(r+1)*n) : :b is the matrix [b0,......,b_s] of dimension (n,(s+1)*m) : :d is the matrix [Id,d_1,......,d_t] of dimension (n,(t+1)*n) : :u is a matrix (m,N), which gives the entry u(:,j)=u_j : :sig is a (n,n) matrix e_{k} is an n-dimensional Gaussian process

with variance I

: :up, yp optional parameter which describe the past. `up=[

u_0,u_{-1},...,u_{s-1}]`; yp=[ y_0,y_{-1},...,y_{r-1}]; ep=[ e_0,e_{-1},...,e_{r-1}]; if they are omitted, the past value are supposed to be zero

: :z z=[y(1),....,y(N)] :

Description

simulation of an n-dimensional armax process A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)

A(z)= Id+a1*z+...+a_r*z^r;  ( r=0  => A(z)=Id)
B(z)= b0+b1*z+...+b_s z^s;  ( s=-1 => B(z)=[])
D(z)= Id+d1*z+...+d_t z^t;  ( t=0  => D(z)=Id)

z et e are in R^n et u in R^m

Method

a state-space representation is constructed and ode with the option “discr” is used to compute z