I have some trouble with understanding how to fit a pure MA(q) (Moving-Average Model of order q) to a time-series in order to forecast future values.

  1. We do not have any past forecasting errors, because we do not have a predictive model yet.
  2. Even if we would initialize the parameters of the MA(q) model randomly, so that we could forecast based on three past forecasting errors, we could not produce residuals for the first three values in the time-series. This means we can not use them to predict the fourth value and so on. I don't see how we can fit a MA(q) model to data.

Can someone please help me understand how Moving-Average models work in practice for forecasting.

  • 1
    $\begingroup$ The short answer is 'maximum likelihood', see for example nber.org/chapters/c12707 $\endgroup$ – JCK Feb 11 at 22:10

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