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Given an MA(2) model

$$X_t = e_t + A_1 e_{t-1} + A_2 e_{t-2}$$

There are cases where there are multiple solutions. Given time series data that we can correctly estimate one solution $(A_1^*,A_2^*)$, how would we calculate the other pairs of coefficients satisfying the model from these?

How does this generalise?

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    $\begingroup$ What's an MA(2) model? $\endgroup$
    – Jeremy Miles
    Dec 16, 2013 at 22:06
  • $\begingroup$ Moving average model, en.wikipedia.org/wiki/Moving_average $\endgroup$
    – rwolst
    Dec 16, 2013 at 22:23
  • $\begingroup$ For every $\theta_j$, $1/\theta_j$ will also work, won't it? But people usually restrict themselves to invertible models, which would restore uniqueness. $\endgroup$
    – Glen_b
    Dec 16, 2013 at 23:32
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    $\begingroup$ Thanks. Acronyms aren't always obvious. To me an MA model is a meta-analysis model. en.wikipedia.org/wiki/Meta-analysis $\endgroup$
    – Jeremy Miles
    Dec 17, 2013 at 0:39

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