# Plotting IR before and after the shock in a unique figure

Hi everyone,

Normally I plot my Impulse Responses and what I observe is just the path followed by the variables immediately after the shock. But how can I manage to plot the path of the variables even when the shock is not yet occured, so that I have a unique figure in which there is not only the path followed by the variables after the shock but also their path immediately before that shock.

Andrew

IRFs analysis is executed so as to observe hypothetical business cycle conducts: deviations from the economy’s steady state; anything before that is hardly germane. Such IRFs are but MA(inf) coefficients pursuant to the AR(1) initial process, provided causality conditions be met by it, plotted against time:

``````y(t)=Ay(t-1)+e(t) - AR(1) (invertible)
y(t)-Ay(t-1)=e(t)
(I-AL)y(t)=e(t)
A(L)y(t)=e(t) - check for causality

min|z(i)|>1 for |I-Az|=0

y(t)=inv[A(L)]e(t)
y(t)=∑Aˆ(j)e(t-j) {with j=0 to inf for ∑, since inv[A(L)]=∑Aˆ(j)Lˆ(j)}
y(t)=Aˆ(0)e(t)+Aˆ(1)e(t-1)+Aˆ(2)e(t-2)+... - MA(inf) (causal)``````

.

The assumption when generating IRFs at order 1 is that the system was in steady state before the shock generating the IRFs hit. All IRFs are plotted relative to the steady state. Thus, the IRFs are simply 0 before the plotted periods. At higher order the issue is more involved as we are talking about Generalized IRFs.

Guys thank you for reply. Actually I know all these things you wrote, I just wondering the way I can plot that situation I described!

Then where is the problem? If you have a shock e and a variable y, you could just use

to plot the 6 periods of 0 preceeding the IRF for y in response to e.