المستخلص: |
Bayesian analysis of Moving Average models is difficult since the likelihood function is highly nonlinear in the parameters, which complicates the prior specification and posterior calculations. Thus, the integrations involved in Bayesian analysis must be done numer¬ically. This is not easy and time consuming especially in the case of the multiparameter models. Approximations can provide a simplification to the likelihood function in order to get standard one step ahead predictive dis¬tribution, namely, the t distribution. Newbold’s approximation is based on expanding the errors as linear functions in the parameters using Taylor’s expansion. Using Taylor’s expansion, Zellner and Reynolds (1987) expanded the errors sum of squares, rather the errors, as a quadratic function in the model coefficients. In this study, first, the problem of predictive analysis of MA models is considered. In order to compare the performance of the above-mentioned approximations in forecasting future observations, the one step ahead predictive densities of the general MA(q) pro¬cesses based on Normal-Gamma prior and Jeffreys’ prior are de¬rived. Second, two Bayesian methods are compared using two com¬parison tools. The first one includes the frequency distributions and summary statistics of the predictive mean. Maximum Abso-lute Difference MAD is the second tool.
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