MA Backcasting in Eviews vs. Box/Jenkins

For technical questions regarding estimation of single equations, systems, VARs, Factor analysis and State Space Models in EViews. General econometric questions and advice should go in the Econometric Discussions forum.

Moderators: EViews Gareth, EViews Moderator

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

MA Backcasting in Eviews vs. Box/Jenkins

Postby jpfeifer » Wed Jan 03, 2018 7:38 am

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

Code: Select all

\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

Code: Select all

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

Code: Select all

\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?

Return to “Estimation”

Who is online

Users browsing this forum: No registered users and 6 guests