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How does TimeSeriesModelFit estimate ARMA parameters?

Posted 7 months ago
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Hi -

I've noticed from comparing several versions (Mathematica, matlab, python) that there can be significant variations in the answers obtained when estimating ARMA parameters. For instance, I can run some data through Mathematica like

model = TimeSeriesModelFit[data,{"ARMA",{1,2}}]

and I will get one answer (usually the best answer). Trying this using a Matlab implementation of an ARMA parameter estimator based on a Kalman filter approach yields not-quite-as-good results in terms of closeness of parameters to their true values. Can anyone enlighten me as to the broad brush strokes of the estimation procedure used in Mathematica ? I couldn't find any documentation that discussed it.

Thanks in advance,

George

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