A note on estimating drift and diffusion parameters from timeseries

Estimating the deterministic drift and stochastic diffusion parameters from discretely sampled data is fraught with the potential for error. We derive a simple way of estimating the error due to the finite sampling rate in these parameters for a univariate system using a straightforward application of the Ito-Taylor expansion. The error is calculated up to first order in the finite sampling time increment Deltat. We then compare the approximate results with the analysis of numerically generated timeseries where the answer is known. Furthermore, a meteorological real world example is discussed. (C) 2002 Elsevier Science B.V. All rights reserved.