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Topic: The ARMA algorithm in MATLAB
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Posts: 3
Registered: 5/24/12
The ARMA algorithm in MATLAB
Posted: May 8, 2013 8:38 AM
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Hi all,

There are many algorithms that can be used to fit a ARMA(p, d, q) model, from the ordinary least square (OLS) and Yule-Walker methods for an AR(p) to the exact maximum likelihood, conditional maximum likelihood and least square methods for an ARMA(p, q). I am wondering what is the algorithm used by MATLAB? I suspect it is the exact maximum likelihood method.

In addition, if all I am interested in is to fit an AR(p) model, would it make any difference to use the exact maximum likelihood method or ordinary least square method?

Thank you in advance.


Besides, the output to run

[fit, VarCov, LogL, info] = estimate(model, data);

where model = arima(p, d, q), and data is 1-D observation.
Number of variables: 33

Objective: @(X)nLogLike(X,Y,E,V,OBJ,AR.Lags,MA.Lags,maxPQ,T,isDistributionT,options,userSpecifiedY0,userSpecifiedE0,userSpecifiedV0)
Gradient: finite-differencing
Hessian: finite-differencing (or Quasi-Newton)
Nonlinear constraints: @(x)nonLinearConstraints(x,LagsAR,LagsSAR,LagsMA,LagsSMA,tolerance)
Nonlinear constraints gradient: finite-differencing

Number of nonlinear inequality constraints: 1
Number of nonlinear equality constraints: 0

Number of linear inequality constraints: 0
Number of linear equality constraints: 0
Number of lower bound constraints: 33
Number of upper bound constraints: 33

Algorithm selected
sequential quadratic programming

End diagnostic information
Norm of First-order
Iter F-count f(x) Feasibility Steplength step optimality
0 34 3.310464e+04 0.000e+00 8.338e+01
1 89 3.310463e+04 0.000e+00 5.585e-04 3.136e-03 5.712e+01
2 145 3.310462e+04 0.000e+00 3.910e-04 2.011e-03 5.637e+01
3 204 3.310462e+04 0.000e+00 1.341e-04 6.956e-04 6.583e+01
4 262 3.310461e+04 0.000e+00 1.916e-04 8.869e-04 3.281e+01
5 318 3.310461e+04 0.000e+00 3.910e-04 1.805e-03 3.657e+01
6 376 3.310461e+04 0.000e+00 1.916e-04 8.227e-04 3.162e+01

I am curious what is F-count, f(x), Feasibility, and First-order optimality?

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