Thread Subject: Variation of ARX model

Hi~! I need to solve a variation of ARX model:
y(t)=C+\sigma a_k*x(t-k)+\sigma b_k*y(t-k)+e(t), where C is a constant.

I looked up in the SYSTEM ID toolbox but didn't find useful function. I wonder if any functions any realize that. Thanks

You mean you need a model with affine term? Note that the model with non
zero C is not a linear model. However, you should be able to use a nonlinear
ARX (idnlarx) model to estimate this; see help for estiamtor NLARX and model
IDNLARX.

Model = nlarx(data, [na nb nk], [])

This model has no nonlinearity (nonlinearity = 'linear'), so it basically
estimates something very similar to a linear ARX model, except that it also
captures the offset (C). The values of the ARX coefficients and the offset
are stored in Model.Nonlinearity.Parameters in fields LinearCoeff and
OutputOffset.

If C is known in advance, it would be better to remove it from y and then
use the detrended data with ARX to estimate a linear model.

-rajiv


"Guanqun " <gqzhang1984@gmail.com> wrote in message
news:go270m$kvc$1@fred.mathworks.com...
> Hi~! I need to solve a variation of ARX model:
> y(t)=C+\sigma a_k*x(t-k)+\sigma b_k*y(t-k)+e(t), where C is a constant.
>
> I looked up in the SYSTEM ID toolbox but didn't find useful function. I
> wonder if any functions any realize that. Thanks