文档介绍：I. Vector Autoregressions
A. Numerical Example
Enders uses a numerical example
(1’’) y(t) = y(t-1) + w(t-1)+ e1(t)
(2’’) w(t) = y(t-1) + w(t-1) + e2(t)
where
e1(t) = ey (t) + ew (t)
e2(t) = ew (t)
and where the variance of e1(t) equals the variance of e2(t), and ey (t) and ew (t) are independent white noise processes.
The white noise processes ey (t) and ew (t) can be simulated and used to generate the error processes e1(t) and e2(t). Then the endogenous variables y(t) and w(t) can be generated. The two standard VAR equationa can be estimated using the simulated endogenous variables y(t) and w(t). They could be estimated using ordinary least squares for each equation. The result is:
y = *y(-1) + *w(-1)
w = *y(-1) + *w(-1)
The residuals from these two estimated equations are ê1(t) and ê2(t). It is not clear from simply looking at the estimated coefficients, etc. how to interpret the behavior of the system. The estimated errors ê1(t) and ê2(t) are correlated so asking how y(t) and w(t) respond to a shock ê1(t), or a shock ê2(t), is not clear in interpretation since the shock or “news” is not unique to either endogenous variable. However, use can be made of the Choleski position, . the relations:
ê1(t) = ey (t) + ew (t)
ê2(t) = ew (t)
where is the correlation between ê1(t) and ê2(t).
The question