What is the difference between a transitory and a permanent shock? In my study of time series regression models in econometrics, we are discussing basic time series regressions and interpreting the effects of shocks in finite distributed lag models. I was wondering what the difference is, in intuitive terms, between a transitory and a permanent shock. According to my understanding at the moment, every shock would be permanent because you cannot undo the past. Wouldn't saying that an effect is transitory be like completely erasing its effect from existence and never accounting for it? I think I am wrong, but I don't know why.
"Permanent shock" is a shock whose effects on current values of a variable never die out in absolute terms. "Transitory shock" is a shock whose effects gradually die out. Consider the simplest one-lag model

$$y_t = \beta y_{t-1} + u_t, \;\;\; y_0 = 0$$

By direct substitution one gets that 

$$y_T = \sum_{t=0}^{T-1}\beta^t u_{T-t} = u_T + \beta u_{T-1} + \beta^2u_{T-2} +...+\beta^{T-1}u_1$$

If $|\beta| &lt;1$ the absolute effect of say shock $u_1$ on $y_T$ diminishes as time passes, $T \uparrow$. While mathematically it doesn't die off completely except at infinity, its absolute contribution decays exponentially.  

On the other hand, if $\beta =1$ (a "unit root" model) then

$$y_T = \sum_{t=0}^{T-1}u_{T-t}=u_T + u_{T-1} + u_{T-2} +...+u_1$$

and no matter how far we move into the future the shock at period $1$ will fully contribute to the value of $y_T$.

Of course, if autocorrelation is strong (high $\beta$) then a "transitory" shock will influence visibly many periods in the future, so it may be "ignored" when examining "long-term" outcomes, but not when one deals with mid-term effects and policy.