Creating a VCEM data generating process

HI: I have to go out so I can't say much but? I wouldn't jump right to
lutkepohl. it's hard to visualize/understanding the matrix case.? I would
think of the bivariate case and then extend it after undersatanding that.?
take the simpler bivariate case ( this is taken directly from eric zivot's
S+Finmetrics book ). generate y_2t = y_2t-1 + v_t where v_t is normal zero
whatever. then let y_1t = b2*y_2t + u_t where u_t is normal zero whatever.
This is a cointegrated system with cointegrating vector (1,-b2). you can
simulate this to visualize the behavior of y_1 and y_2 over time. If you
don't have eric's book, I can fax you the two pages tomorrow. Generally
speaking, unless you're quite familar with this material, I would start
out with something along the level of Eric's book or Enders and then go to
Lutkepohl after that. I really gotta run. Hopefully someone else can help
you more but let me know if you want me to fax you the pages. it's 421-428
if you have the book. On Jun 28, 2009, RON70
<ron_michael70 at yahoo.com> wrote: 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? statquant wrote: > > 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. > Thanks and regards, -- View this
message in context: >
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