Dear all,

I am trying to write an R function that can estimate Transfer functions *with additive noise* i.e.

Y_t = \delta^-1(B)\omega(B)X_{t-b} + N_t

where B is the backward shift operator, b is the delay and N_t is a noisy component that can be modelled as an ARMA process. The parameters to both the impulse response function and the ARMA noisy component need to be estimated simultaneously.

I have got as far as being able to compute the residual noise, a_t. However, I am slightly confused about what to do next. Reading Box-Jenkins, 1976 (pp. 391) they state the following

"....However, it seems simplest to work with a standard nonlinear least squares computer program in which the derivatives are determined numerically and an option is available of 'constrained iteration' to prevent instability. It is then only necessary to program the computation of a_t itself......."

I know that there is a 'nls' function in R but I really do not have a clue about how to use it in this situation. Perhaps Box-Jenkins are confusing me with their last sentance with regard to the a_t's - is this really possible?

If anyone could help me on this I would be most grateful. I know this is not exactly an R question, but to the best of my knowledge there is no transfer function estimation method in R at the moment and so this might be a nice additional feature?

Kind regards,

Sam. 


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