below is a ink related to what Derek said below.<br /><a href="http://www.puc-rio.br/marco.ind/revers.html"><br /><br />http://www.puc-rio.br/marco.ind/revers.html</a><br /><br /><br /><p>On Jun 17, 2009, <strong>Schaeffer, Derek BGI SF</strong> <Derek.Schaeffer@barclaysglobal.com> wrote: </p><div class="replyBody"><blockquote style="padding-left: 1ex; margin: 0pt 0pt 0pt 1.8ex; border-left: #267fdb 2px solid"><br />Hi Marco,<br /><br />The discrete time Vasicek model at partition size dt (e.g. 1/252) is<br />given by:<br /><br />X(t) - X(t-dt) = [a*b] * dt - [b * X(t-dt)] * dt + s_e * e, e ~<br />N(0,1)<br /><br />Run the following regression:<br /><br />X(t) = A + B X(t-1) + v, v ~ N(0,s_v^2)<br /><br />The continuous-time parameters can be recovered from the regression<br />estimates using:<br /><br />b = -A/B<br />a = -ln(1 + B)/dt<br />s_e = s_v * sqrt(2 * ln(1 + B) / dt) / sqrt( (1+B)^2 - 1)<br /><br />Best,<br />Derek M. Schaeffer, Ph.D. <br />Principal <br />Senior Research Officer<br /><br />TEL 415 894 6427<br />CELL 415 516 9558<br />FAX 415 618 1824<br /><a href="mailto:derek.schaeffer@barclaysglobal.com" target="_blank" class="parsedEmail">derek.schaeffer@barclaysglobal.com</a><br /><br />Barclays Global Investors 400 Howard Street San Francisco, CA 94105<br /><br /><br /><br />-----Original Message-----<br />From: <a href="mailto:r-sig-finance-bounces@stat.math.ethz.ch" target="_blank" class="parsedEmail">r-sig-finance-bounces@stat.math.ethz.ch</a><br />[mailto:<a href="mailto:r-sig-finance-bounces@stat.math.ethz.ch" target="_blank" class="parsedEmail">r-sig-finance-bounces@stat.math.ethz.ch</a>] On Behalf Of Zanella<br />Marco<br />Sent: Wednesday, June 17, 2009 9:41 AM<br />To: <a href="mailto:r-sig-finance@stat.math.ethz.ch" target="_blank" class="parsedEmail">r-sig-finance@stat.math.ethz.ch</a><br />Subject: [R-SIG-Finance] Vasicek model estimation via linear regression<br /><br />Hi,<br />I have to check mean reversion with a Vasicek model for a time series.<br />As you certainly know Vasicek process is discribed by following formula:<br /><br />dXt = a(b-Xt)dt + sdWt (1) <br /><br /><a href="http://en.wikipedia.org/wiki/Vasicek_model" target="_blank" class="parsedLink">http://en.wikipedia.org/wiki/Vasicek_model</a><br /><br />To estimate the parameters in my data I can use this expression:<br /><br />Xt - Xt-1 = a(b-Xt-1)Dt + se (2) <br /><br />where:<br />Xt: time series at time t<br />Xt-1: time series at time t-1<br />a: unknown parameter<br />b: unknown parameter<br />Dt: in my case I can assimilate it = 1<br />S: standard deviation<br />e: error ~N(0,1)<br /><br />Basically, I want to estimate unknown parameters a and b using a linear<br />regression. Usually I work on linear regression with lm() function but I<br />don't undertand how formulate my (2) model in to lm command. Can anyone<br />give me some suggestions?<br /><br />Thanks in advance.<br /><br />Regards,<br /><br />Marco<br /><br />____________________________________________________________<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 /><br />This message and any attachments are confidential, propr...{{dropped:14}}<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 /></blockquote></div>