Creating a VCEM data generating process

Thanks Statquant for this reply, however it is still not clear. Suppose I
have following theoretical DGP :

deltaY[t] = alpha + PI * Y[t-1] + A1 * deltaY[t-1] + A2 * deltaY[t-2] + A3 *
deltaY[t-3] + epsilon[t]

Next suppose, I have chosen some particular matrices as coefficient matrices
and taken them as population value. However how can I make it sure that DGP
has some unit root, with those arbitrarily chosen coef. matrices? My finding
was that, if I chose some arbitrary matrices and then solve the ch.
equation, I do not get some solutions as 1 and rests are outside the range
[-1, 1].

The steps that I thought of are :
1. Choose some matrices for alpha, PI, A1, A2, A3 (I need to find those!!!)
such that ch. equation gives some roots as "1" & rests are outside the range
[-1, 1].
2. Generate 1,000 realizations each with size 100 (say)
3. For each realization, re-estimate the coefficients.
4. Analyze the distribution of the coef.

Someone might find it as homework, however it is not. Currently I am
studying Lutkepohl and some asymptotic dist. are discussed here. I want to
get some empirical match.

Any idea?

hi ron : the simple vecm is 1) delta y_t = delta x_t + alpha(y_t-1 -
beta*x_t-1) + epsilon_yt? ( but check this to make sure ). so, first
generate x_t's that are I(1) by generating x_t = x_t -1 + epsilon_xt Then.
given the x_t's,? pick some beta and an an alpha, and generate the y_t's
based? on 1). this will give you y_t and x_t? that are I(1) and
cointegrated by definition. the multi vecm is more complex but the idea is
the same. On Jun 28, 2009, RON70 <ron_michael70 at yahoo.com> wrote: Hi
all, Can anyone here please help me how to create a DGP which corresponds
to VECM (Vector error correction) ? Actually I want to define a arbitrary
VECM as a DGP and then study the properties of it's realizations. However
I can not construct an arbitrary VECM from my own, especially it's
coefficients, which lead to strictly I(1) process of individual variable.
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