ARMA model for temperature simulation

Hello, I really checked all relevant posts and I could not find the right answer. I'm also not an expert in ARMA models so please apologize my (maybe) naive question. I want to model daily temperature using an ARMA or AR model. So I think I know how to fit it now (in the system identification toolbox). So I fitted an ARMA(1,1) model to 31 January temperature values:

model=armax(JanTemp(:,1),[1 1]);

Discrete-time IDPOLY model: A(q)y(t) = C(q)e(t)

A(q) = 1 - 0.9658 q^-1

C(q) = 1 - 0.653 q^-1

But how can I now simulate from this fitted model stochastically? What I want to do is simulating say 31 artifical January days that follow the statistical behaviour of my historical dataset but represent a new realization? I know there is a simulation routine "sim" but I got stuck when trying to understand the documentation.

I unfortunately don't have the econometrics toolbox which seems to have some ARMA algorithms.

Your help would be highly appreciated! - Peter

Answer 1

[Rajiv Singh]

See SIM and SIMSD functions in System Identification Toolbox.

When using SIM, add the 'noise' qualifier as input argument to perform stochastic simulation, as in:

y = sim(model, zeros(100,0), 'noise')

Post examples of things you tried, then I may be able to give you more targeted advice.

rajiv

Answer 2

[grapevine]

If you have enough measurements of the inputs and the outputs of the process you might perform a system identification There are severals techniques :

Least means squares identification it's the easy one, I return a linear estimation of the transfer function

http://www.mathworks.nl/help/toolbox/ident/ref/armax.html

http://www.mathworks.nl/help/toolbox/ident/ref/arx.html

http://www.mathworks.com/matlabcentral/fileexchange/3649-lms-algorithm-demo

Luenberger observer it returns an estimation of the state variables

http://cse.lab.imtlucca.it/~bemporad/teaching/ac/pdf/06b-estimator.pdf

http://inst.eecs.berkeley.edu/~ee128/fa08/labs/EECS128_lab5b.pdf

Kalman filter it's a powerful algorithm which uses a series of measurements observed over time, containing noise, and produces and estimation of the states

http://www.mathworks.com/matlabcentral/fileexchange/18189

http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html

 <http://personnel.supaero.fr/alazard-daniel/Pdf/cours_Kalman.pdf> (if you speak French)

you could be interested at this Matlab toolbox

http://www.mathworks.nl/products/sysid/

and a this function: * tfest*

http://www.mathworks.nl/help/toolbox/ident/ref/tfest.html

wish u the best