[R] estimation of drift of continuous random walk

[Adrian Trapletti]

  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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