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.
[[alternative HTML version deleted]]
"Kemp S E (Comp)" <sekemp at glam.ac.uk> writes:> 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?I'm not sure I'd trust any computer recommendation from 1976, no matter how famous the authors are. However, the hint would lead me to consider the optim() function. -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
> From: Peter Dalgaard > > "Kemp S E (Comp)" <sekemp at glam.ac.uk> writes: > > > 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? > > I'm not sure I'd trust any computer recommendation from 1976, no > matter how famous the authors are. However, the hint would lead me to > consider the optim() function.My copy of Box/Jenkins/Reinsel (1994, 3rd ed.) has exactly the same passage on page 430 (except an reference to chapter 7)... Andy> -- > O__ ---- Peter Dalgaard Blegdamsvej 3 > c/ /'_ --- Dept. of Biostatistics 2200 Cph. N > (*) \(*) -- University of Copenhagen Denmark Ph: > (+45) 35327918 > ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: > (+45) 35327907 > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >