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 ).<br /><br />generate y_2t = y_2t-1 + v_t where v_t is normal zero whatever.<br /><br />then let <br /><br />y_1t = b2*y_2t + u_t where u_t is normal zero whatever.<br /><br />This is a cointegrated system with cointegrating vector (1,-b2). you can simulate this to visualize the behavior<br />of y_1 and y_2 over time. If you don't have eric's book, I can fax you the two pages tomorrow.<br /><br />Generally speaking, unless you're quite familar with this material, I would start out with something along the<br />level of Eric's book or Enders and then go to Lutkepohl after that. I really gotta run. Hopefully someone else can help you<br />more but let me know if you want me to fax you the pages. it's 421-428 if you have the book.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><p>On Jun 28, 2009, <strong>RON70</strong> <ron_michael70@yahoo.com> wrote: </p><div class="replyBody"><blockquote style="border-left: 2px solid #267fdb; margin: 0pt 0pt 0pt 1.8ex; padding-left: 1ex"><br />Thanks Statquant for this reply, however it is still not clear. Suppose I<br />have following theoretical DGP :<br /><br />deltaY[t] = alpha + PI * Y[t-1] + A1 * deltaY[t-1] + A2 * deltaY[t-2] + A3 *<br />deltaY[t-3] + epsilon[t]<br /><br />Next suppose, I have chosen some particular matrices as coefficient matrices<br />and taken them as population value. However how can I make it sure that DGP<br />has some unit root, with those arbitrarily chosen coef. matrices? My finding<br />was that, if I chose some arbitrary matrices and then solve the ch.<br />equation, I do not get some solutions as 1 and rests are outside the range<br />[-1, 1].<br /><br />The steps that I thought of are :<br />1. Choose some matrices for alpha, PI, A1, A2, A3 (I need to find those!!!)<br />such that ch. equation gives some roots as "1" & rests are outside the range<br />[-1, 1].<br />2. Generate 1,000 realizations each with size 100 (say)<br />3. For each realization, re-estimate the coefficients.<br />4. Analyze the distribution of the coef.<br /><br />Someone might find it as homework, however it is not. Currently I am<br />studying Lutkepohl and some asymptotic dist. are discussed here. I want to<br />get some empirical match.<br /><br />Any idea?<br /><br /><br />statquant wrote:<br />> <br />> hi ron : the simple vecm is 1) delta y_t = delta x_t + alpha(y_t-1 -<br />> beta*x_t-1) + epsilon_yt ( but check this to make sure ). so, first<br />> generate x_t's that are I(1) by generating x_t = x_t -1 + epsilon_xt Then.<br />> given the x_t's, pick some beta and an an alpha, and generate the y_t's<br />> based on 1). this will give you y_t and x_t that are I(1) and<br />> cointegrated by definition. the multi vecm is more complex but the idea is<br />> the same. On Jun 28, 2009, RON70 &lt;<a href="mailto:ron_michael70@yahoo.com" target="_blank" class="parsedEmail">ron_michael70@yahoo.com</a>&gt; wrote: Hi<br />> all, Can anyone here please help me how to create a DGP which corresponds<br />> to VECM (Vector error correction) ? Actually I want to define a arbitrary<br />> VECM as a DGP and then study the properties of it's realizations. However<br />> I can not construct an arbitrary VECM from my own, especially it's<br />> coefficients, which lead to strictly I(1) process of individual variable.<br />> Thanks and regards, -- View this message in context:<br />> <a href="http://www.nabble.com/Creating-a-VCEM-data-generating-process-tp24243230p24243230.html" target="_blank" class="parsedLink">http://www.nabble.com/Creating-a-VCEM-data-generating-process-tp24243230p24243230.html</a><br />> Sent from the Rmetrics mailing list archive at Nabble.com.<br />> _______________________________________________<br />> <a href="mailto:R-SIG-Finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">R-SIG-Finance@stat.math.ethz.ch</a> mailing list<br />> <a href="https://stat.ethz.ch/mailman/listinfo/r-sig-finance" target="_blank" class="parsedLink">https://stat.ethz.ch/mailman/listinfo/r-sig-finance</a> -- Subscriber-posting<br />> only. -- If you want to post, subscribe first. <br />> <br />> <br />> _______________________________________________<br />> <a href="mailto:R-SIG-Finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">R-SIG-Finance@stat.math.ethz.ch</a> mailing list<br />> <a href="https://stat.ethz.ch/mailman/listinfo/r-sig-finance" target="_blank" class="parsedLink">https://stat.ethz.ch/mailman/listinfo/r-sig-finance</a><br />> -- Subscriber-posting only.<br />> -- If you want to post, subscribe first.<br />> <br /><br />-- <br />View this message in context: <a href="http://www.nabble.com/Re%3A--R-sig-finance--Creating-a-VCEM-data-generating%09process-tp24244254p24245075.html" target="_blank" class="parsedLink">http://www.nabble.com/Re%3A--R-sig-finance--Creating-a-VCEM-data-generating%09process-tp24244254p24245075.html</a><br />Sent from the Rmetrics mailing list archive at Nabble.com.<br /><br />_______________________________________________<br /><a href="mailto:R-SIG-Finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">R-SIG-Finance@stat.math.ethz.ch</a> mailing list<br /><a href="https://stat.ethz.ch/mailman/listinfo/r-sig-finance" target="_blank" class="parsedLink">https://stat.ethz.ch/mailman/listinfo/r-sig-finance</a><br />-- Subscriber-posting only.<br />-- If you want to post, subscribe first.</blockquote></div>