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We shall show that for {\it any} $MA(2)$ process (apart from those withcoefficients $\theta_1,\theta_2 $ lying on certain line-segments) there is {\itone and only one invertible} $MA(2)$ process with the {\it same}autocovariances $\gamma_0,\gamma_1,\gamma_2$. It is this invertible versionwhich computer-packages fit, regardless, even if data came from anon-invertible $MA(2)$ process. This has consequences for prediction from afitted process, inasmuch as such prediction would seem to be inappropriate. Weexpress the coefficients $\theta_1,\theta_2 $ of the invertible version interms of $\gamma_0,\gamma_1,\gamma_2$ explicitly using analytical reasoning,following a graphical approach of Sbrana (2012) which indicates this resultwithin the invertibility region. We also express $(\theta_1,\theta_2)$ in thenon-invertibility region.

Explicit Form of Coefficients in any MA(2) Process