# [R-SIG-Finance] [R-sig-finance] Creating a VCEM data generating process

RON70 ron_michael70 at yahoo.com
Sun Jun 28 23:11:00 CEST 2009

```Thank you so much for this. If you dont have any problem, can you please send
them here ron_michael70 at yahoo.com ?

Thanks and regards,

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