5
$\begingroup$

Mathematica has extensive support for time series, but I haven't found anything with exogenous signal. Is it possible to fit a time series with exogenous signal in Mathematica? For example identifying a discrete linear system?

For example, let's suppose there is a heat exchange with inputs $u_1$ (flow) and $u_2$ (input temperature) and the output $y$ as the output temperature. The problem in concern in to fit an ARMA model with exogenous signal $u_1$ and $u_2$.

Given the sampled signals $u_1(k)$, $u_2(k)$ and $y(k)$, $k=1...n$. Find the vectors $a=[a_1,...a_{n_a}]$, $b=[b_1,...b_{n_b}]$ and $c=[c_1,...c_{n_c}]$ such that the process is modeled by:

$$y(k)=\sum_{i=1}^{n_a} a_iy(k-i)+\sum_{i=1}^{n_b} b_iu_1(k-i)+\sum_{i=1}^{n_c} c_iu_2(k-i)+\varepsilon(k-1)$$ where $\varepsilon$ is a noise.

This is a simple and common problem and it is strange that in Mathematica there is ARMA process but not ARMAX process.

$\endgroup$
2
  • $\begingroup$ What does "exogenous signal" mean? Can you provide a sample data set and your expected output? $\endgroup$
    – MarcoB
    Jan 27, 2017 at 16:01
  • $\begingroup$ I have added better explanation and an example. it's much clear now. $\endgroup$
    – Lie Pablo
    Jan 28, 2017 at 8:07

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.