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
2012-6-27
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
2012-6-27
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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