# [R] estimation of drift of continuous random walk

Fri Jul 20 18:31:00 CEST 2001

```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,

-----Original Message-----
From: Patrick Foley [mailto:patfoley at csus.edu]
Sent: Thursday, July 19, 2001 8:40 PM
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] estimation of drift of continuous random walk

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

> 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,
>
> --------------------------------------------------
> 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
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._.
_._

--------------------------------------------------
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
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._

```