# How does TimeSeriesModelFit estimate ARMA parameters?

Posted 5 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