ARMA model for temperature simulation
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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
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Rajiv Singh
le 27 Juin 2012
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
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grapevine
le 27 Juin 2012
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
Luenberger observer it returns an estimation of the state variables
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://personnel.supaero.fr/alazard-daniel/Pdf/cours_Kalman.pdf> (if you speak French)
you could be interested at this Matlab toolbox
and a this function: * tfest*
wish u the best
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