## MA Backcasting in Eviews vs. Box/Jenkins

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jpfeifer
Posts: 3
Joined: Wed Apr 08, 2015 11:47 am

### MA Backcasting in Eviews vs. Box/Jenkins

According to the Eviews help, MA terms are backcasted by running the forward model backwards in time:

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\tilde \epsilon_t=u_t-\theta_1*\tilde \epsilon_{t+1}-...-\theta_q*\tilde \epsilon_{t+q}

with \tilde \epsilon_{T+i}= for i>0. This allows computing

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{\tilde \epsilon_{0},...,\tilde \epsilon_{-(q-1)}
. The help seems to suggest that the \tilde \epsilon are then used in the backward model

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\hat \epsilon_t=u_t-\theta_1*\hat \epsilon_{t-1}-...-\theta_q*\hat \epsilon_{t-q}

i.e. the \tilde \epsilon_{i}, i<1 are used as the \hat \epsilon_{i}. But the reference is the the Box/Jenkins (1970) book. In its 2016 edition, Chapter 7.1.4, the procedure seems to be quite different as the forward and backward model deliver two different, distinct sets of innovations. They therefore do not allow using the innovations from the forward model in the backward model. To solve this problem, they backcast the u_t for t={0,..,q-1} using the backcasts for \tilde \epsilon_t and employ that \tilde \epsilon_{i}=0,i<1 due to them being independent from u_t. These u_t, t<1 are then used in the backward model to run a forward recursion with \hat \epsilon_{i}=0 for i<q-1 due to independence. This then allows computing {\hat \epsilon_{0},...,\hat \epsilon_{-(q-1)}.

So what exactly does Eviews do here?