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
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