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The ARMA algorithm in MATLAB
Posted:
May 8, 2013 8:38 AM


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 YuleWalker 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.
Best, Ye
Besides, the output to run
[fit, VarCov, LogL, info] = estimate(model, data);
where model = arima(p, d, q), and data is 1D observation.  Number of variables: 33
Functions Objective: @(X)nLogLike(X,Y,E,V,OBJ,AR.Lags,MA.Lags,maxPQ,T,isDistributionT,options,userSpecifiedY0,userSpecifiedE0,userSpecifiedV0) Gradient: finitedifferencing Hessian: finitedifferencing (or QuasiNewton) Nonlinear constraints: @(x)nonLinearConstraints(x,LagsAR,LagsSAR,LagsMA,LagsSMA,tolerance) Nonlinear constraints gradient: finitedifferencing
Constraints 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 Firstorder Iter Fcount 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 5.585e04 3.136e03 5.712e+01 2 145 3.310462e+04 0.000e+00 3.910e04 2.011e03 5.637e+01 3 204 3.310462e+04 0.000e+00 1.341e04 6.956e04 6.583e+01 4 262 3.310461e+04 0.000e+00 1.916e04 8.869e04 3.281e+01 5 318 3.310461e+04 0.000e+00 3.910e04 1.805e03 3.657e+01 6 376 3.310461e+04 0.000e+00 1.916e04 8.227e04 3.162e+01
I am curious what is Fcount, f(x), Feasibility, and Firstorder optimality?



