How do we find out the long term and short term effect of estimators on AR model?
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According to Hamilton (1994), page 1-5:
suppose a process where: $y_{t} = b \times y_{t-1} + w_{t}$
Where $y_{t-1}$ is the realisation in the previous period and $w_{t}$ is some random innovation.
The long run effect therefore is the effect on $y_{t+1}$ from a permanent increase in $w$. Hence the long-run effect is ${1}/{(1-b)}$ for this special case (or the expected value of the function). For the short run effect I cannot find a proper source right now but I remember it being the coefficient ($b$ in this case).
However, as far as I know the term is far more common for Vector Error Correction models. Hope this helps a bit.
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$\begingroup$ Please improve your question. What is w? What is theta? See the FAQ, the answers in this site should be as self-sufficient as possible. $\endgroup$– mpiktasCommented Dec 16, 2011 at 13:46
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$\begingroup$ @mpiktas: hope it is more understandable now - i was in a hurry before - sorry. $\endgroup$– SebCommented Dec 16, 2011 at 13:56