User`s guide

Identifying State-Space Models
Specify the structure matrix values, as follows:
• Set a
NaN value to flag free parameters at the corresponding locations i n
A, B, C, D, K,andx0.
• Specify the values of fixed parameters at the corresponding locations in
A, B, C, D, K,andx0.
For example, suppose that you constructed a nominal state-space model
m
with the following A matrix:
A = [2 0; 0 3]
Suppose you want to fix A(1,2)=A(2,1)=0. Tospecifytheparametersyou
want to fix, enter their values at the corresponding locations in the structure
matrix
As:
m.As = [NaN 0; 0 NaN]
The estimation algorithm only estimates the parameters in A that have a
NaN value in As.
Finally, use
pem to estimate the model, as described in “How to Estimate
State-Space Models at the C ommand Line ” on page 3-87.
Use physical insight, whe n ever p os sib le , to initialize the parame te rs for
the iterative search algorithm. Because it is possible that the numerical
minimization gets stuck in a local minimum, try several different initialization
values for the parameters. For random i n itia l ization, use the
init command.
When the model s tructure contains p aram eters with different orders of
magnitude, try to scale the variables so that the parameters are all roughly
thesamemagnitude.
The iterative search computes gradients of the prediction errors with respect
to the parameters using numerical differentiation. The step size is specified
by the
nuderst M-file. The default step size is equal to 10
–4
times the absolute
value of a parameter or equal to 10
–7
, whichever is larger. To specify a
different step size, edit the
nuderst M-file.
3-95