Prediction confidence intervals using a state-space model

4 views (last 30 days)
Hello all,
Suppose one has estimated a state-space model using the following.
id = iddata(data',[],Ts);
sys = ssest(id, 2, 'Ts',id.Ts, 'DisturbanceModel','estimate');
Where data is a (output-only) time-series. Then, forecasting is as follows.
frc = forecast(sys, id, K);
My question is, how can one get the confidence intervals of the forecasted output, given that the system has uncertainties? The uncertainties of the model can be obtained with
[pvec, pvec_sd] = getpvec(sys) % parameter values and std deviations
An overview of the identified system is available with
present(sys)
Thank you in advance!

Accepted Answer

Rajiv Singh
Rajiv Singh on 7 Jun 2013
For discrete-time systems, the forecasting model is same as the simulation (original) model. So you can use commands such as SIM and SIMSD for uncertainty analysis.
For generating response uncertainty bounds by Gauss Approximation formula:
[frc,x0e] = forecast(sys, id, K);
zu = iddata([],zeros(K,0), id.ts, 'tstart',frc.tstart);
opt = simOptions('InitialCondition',x0e);
[y,ysd] = sim(sys, zu, opt);
t = y.SamplingInstants;
plot(t, y.y, t, y.y+ysd.y, 'r', t, y.y-ysd.y,'r')
For Monte-Carlo simulation of the estimated model:
opt = simsdOptions('InitialCondition',x0e);
simsd(sys, zu, 20, opt)

More Answers (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!