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As a beginner in Bayesian estimation I believe I have made progress on the understanding of the estimation process.

However, after the estimation and evaluation/comparison of the models I find myself stuck in the understanding of the forecasting issue.

For example, I estimate a simple linear regression model ,like this one: $Y_t = \alpha_0 + \alpha_1 X_t + \epsilon$, by various methods: OLS regression,median regression and Bayesian Methods.

Now comes my question: In the Bayesian literature I´ve have seen several interesting ways to do the forecasting, for example, i could put in a framework of dynamic linear models.

However, I wonder how can I do a simple exercise of forecasting without resorting to dynamic linear models. In fact, I would like to understand the passage from the Bayesian estimation to forecasting exercises. In my mind, i would have to "forecast" the posteriors distribution for each time, t, t=1,2,3,4.., 10. But then others doubts comes to my mind.

Could you help me?

Thanks a lot.

Linkman
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  • Thanks, Tim! It would be good delete my post? – Linkman Oct 23 '15 at 13:25
  • If the other thread answer your question - it is your decision. However this site has a build-in mechanism to deal with duplicates, so generally you do not have to worry about it because duplicate threads are semi-automatically closed and linked to related questions. – Tim Oct 23 '15 at 13:27
  • Ok, Tim. One of my doubts is where this `ynew` coe from? How can i construct this `ynew`? – Linkman Oct 23 '15 at 13:32
  • The answer is here [link](https://en.wikipedia.org/wiki/Posterior_predictive_distribution) ? – Linkman Oct 23 '15 at 13:34
  • `ynew` does not exist :) in the example provided in the linked thread `ynew` are values randomly drawn from the posterior. – Tim Oct 23 '15 at 13:35
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    Forecasting is estimation! You build a posterior on a future value instead of (or in addition to) a posterior on the permanent parameters of the model. In other words, everything should be done at the same rather than "after estimation". – Xi'an Oct 23 '15 at 13:39

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