Dear R-Users,
I have the following problem to solve and I wonder if there are means in R
that can help me.
At irregular time intervals I observe a random walk process, Y, with
time-varying drift. I assume that the drift, D, is a (linear) function of
some parameter X. The goal is to estimate D(X).
I could regress Y_{t+dt} - Y_{t} ~ X, but it's probably not appropriate
since Var(Y_{t+dt} - Y_{t}) is not constant (actually in theory it is
proportional to dt).
Any suggestions?
Thank you,
Vadim
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Vadim, If I understand you correctly, the maximum likelihood estimator for the drift term is D = (Y(T) -Y(0))/T where you have data Y(t) t = 0 ... T and constant drift D and diffusion coefficients. Therefore if there is variable drift (but constant diffusion), one crude estimate of D(X) would be to use this in chunks in your regression and then smooth it at the end. If you believe that D is a linear function of X then why not a regression of (Y(t +dt)-Y(t))/dt on X(t)? Patrick Foley patfoley at csus.edu Vadim Ogranovich wrote:> Dear R-Users, > > I have the following problem to solve and I wonder if there are means in R > that can help me. > > At irregular time intervals I observe a random walk process, Y, with > time-varying drift. I assume that the drift, D, is a (linear) function of > some parameter X. The goal is to estimate D(X). > > I could regress Y_{t+dt} - Y_{t} ~ X, but it's probably not appropriate > since Var(Y_{t+dt} - Y_{t}) is not constant (actually in theory it is > proportional to dt). > > Any suggestions? > > Thank you, > Vadim > > -------------------------------------------------- > DISCLAIMER > This e-mail, and any attachments thereto, is intended only for use by the > addressee(s) named herein and may contain legally privileged and/or > confidential information. If you are not the intended recipient of this > e-mail, you are hereby notified that any dissemination, distribution or > copying of this e-mail, and any attachments thereto, is strictly prohibited. > If you have received this e-mail in error, please immediately notify me and > permanently delete the original and any copy of any e-mail and any printout > thereof. > > E-mail transmission cannot be guaranteed to be secure or error-free. The > sender therefore does not accept liability for any errors or omissions in > the contents of this message which arise as a result of e-mail transmission. > > NOTICE REGARDING PRIVACY AND CONFIDENTIALITY > > Knight Trading Group may, at its discretion, monitor and review the content > of all e-mail communications. > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- > r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
1. Date: Thu, 19 Jul 2001 19:56:34 -0500
2. From: Vadim Ogranovich <vograno at arbitrade.com>
3. Subject: [R] estimation of drift of continuous random walk
4.
5. Dear R-Users,
6.
7. I have the following problem to solve and I wonder if there are
means in R
8. that can help me.
9.
10. At irregular time intervals I observe a random walk process, Y,
with
11. time-varying drift. I assume that the drift, D, is a (linear)
function of
12. some parameter X. The goal is to estimate D(X).
13.
14. I could regress Y_{t+dt} - Y_{t} ~ X, but it's probably not
appropriate
15. since Var(Y_{t+dt} - Y_{t}) is not constant (actually in theory it
is
16. proportional to dt).
(If the model is correctly specified) the above OLS regression should
give a consistent estimator for the drift. Using a WLS regression (in R
use lm(...,weights=...)) with weights proportional to 1/Var(Y_{t+dt} -
Y_{t}) = 1/dt (in this example) should produce a "better" estimator.
1.
2. Any suggestions?
3.
4. Thank you,
5. Vadim
6.
7.
best
Adrian
--
Dr. Adrian Trapletti Phone : +41 (0)1 994 56 30
Wildsbergstrasse 31 Fax : +41 (0)1 994 56 33
CH-8610 Uster, Switzerland Email : a.trapletti at bluewin.ch
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Thank you to Patrick Foley and Adrian Trapletti. Their compiled answer is: a) fix model specification and regress (Y(t+dt) - Y(t))/dt ~ X(t) // originally I forgot to devide by dt b) use weighted regression with weights = 1/Var((Y(t+dt) - Y(t))/dt) = dt. Thanks, Vadim -----Original Message----- From: Patrick Foley [mailto:patfoley at csus.edu] Sent: Thursday, July 19, 2001 8:40 PM To: Vadim Ogranovich Cc: r-help at stat.math.ethz.ch Subject: Re: [R] estimation of drift of continuous random walk Vadim, If I understand you correctly, the maximum likelihood estimator for the drift term is D = (Y(T) -Y(0))/T where you have data Y(t) t = 0 ... T and constant drift D and diffusion coefficients. Therefore if there is variable drift (but constant diffusion), one crude estimate of D(X) would be to use this in chunks in your regression and then smooth it at the end. If you believe that D is a linear function of X then why not a regression of (Y(t +dt)-Y(t))/dt on X(t)? Patrick Foley patfoley at csus.edu Vadim Ogranovich wrote:> Dear R-Users, > > I have the following problem to solve and I wonder if there are means in R > that can help me. > > At irregular time intervals I observe a random walk process, Y, with > time-varying drift. I assume that the drift, D, is a (linear) function of > some parameter X. The goal is to estimate D(X). > > I could regress Y_{t+dt} - Y_{t} ~ X, but it's probably not appropriate > since Var(Y_{t+dt} - Y_{t}) is not constant (actually in theory it is > proportional to dt). > > Any suggestions? > > Thank you, > Vadim > > -------------------------------------------------- > DISCLAIMER > This e-mail, and any attachments thereto, is intended only for use by the > addressee(s) named herein and may contain legally privileged and/or > confidential information. If you are not the intended recipient of this > e-mail, you are hereby notified that any dissemination, distribution or > copying of this e-mail, and any attachments thereto, is strictlyprohibited.> If you have received this e-mail in error, please immediately notify meand> permanently delete the original and any copy of any e-mail and anyprintout> thereof. > > E-mail transmission cannot be guaranteed to be secure or error-free. The > sender therefore does not accept liability for any errors or omissions in > the contents of this message which arise as a result of e-mailtransmission.> > NOTICE REGARDING PRIVACY AND CONFIDENTIALITY > > Knight Trading Group may, at its discretion, monitor and review thecontent> of all e-mail communications. > >-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. -.-> r-help mailing list -- Readhttp://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html> Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch >_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._. _._ -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. -.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._. _._ -------------------------------------------------- DISCLAIMER This e-mail, and any attachments thereto, is intended only for use by the addressee(s) named herein and may contain legally privileged and/or confidential information. If you are not the intended recipient of this e-mail, you are hereby notified that any dissemination, distribution or copying of this e-mail, and any attachments thereto, is strictly prohibited. If you have received this e-mail in error, please immediately notify me and permanently delete the original and any copy of any e-mail and any printout thereof. E-mail transmission cannot be guaranteed to be secure or error-free. The sender therefore does not accept liability for any errors or omissions in the contents of this message which arise as a result of e-mail transmission. NOTICE REGARDING PRIVACY AND CONFIDENTIALITY Knight Trading Group may, at its discretion, monitor and review the content of all e-mail communications. -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._