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Abstract
This study is mainly interested in the estimation of different time series models. The posterior density is the bayesian tools to implement estimation. Three well known approximations are used. The approximations were proposed by (newbold (1973)), (zellner and reynolds (1978)) and (broemeling and shaarawy (1988)), denoted by (N), (Z - R) and (B - S) respectively. Different mixed seasonal time series of different lengths and values of the parameters as well as different goodness criteria are used for illustration. The study applied the three approximations of seasonal ARMA models numerically. All the three approximate posterior densities of the coefficient’s vector follow multivariatet distributions with the same degrees of freedom. On the other hand, the three approximate posterior densities of the precision follow gamma distributions whatever the prior be either normal - gamma or Jeffreys’. The study showed that the MAD values of the three approximate posterior densities increases with the increase in the time series length ’n’. The moments of the exact and the three approximate posterior densities are approximately identical