On Bayes Estimation of the First Order Moving Average Model

In this work, Bayes estimation of the first order moving average model (MA(1)) were studied. Theoretical justification of the Bayes estimates based on the estimated innovations is given. The convergence of Bayes and maximum likelihood estimates are examined via simulation using different parameter values. Also, Bayes estimates were determined when the model is invertible using the estimated innovations. For long series lengths, it has been noted that the Bayes estimate of θ of invertible MA(1) model assuming uniform prior on θ and inverted gamma prior on σ² equals the Bayes estimate of θ for noninvertible MA(1) model. Generally, the simulation results showed that the performance of the Bayes estimates using estimated innovations depends on the values of θ within the invertibility region. As expected, we note that the performance of the maximum likelihood and Bayes estimates are equally likely for long series lengths.