Prediction-based estimating functions for diffusion processes with measurement noise

Kim Nolsøe, Jan Nygaard Nielsen, Henrik Madsen (

For a copy of this paper, either Abstract:

The prediction-based estimating functions proposed by Sorensen (1999) are generalized to facilitate parameter estimation in discretely observed stochastic differential equations, where the observations are corrupted by additive white noise. The new class of estimating functions has most of the nice properties of martingale estimating functions. However, they may be applied when no obvious or easily calculated martingales exist. Simple expressions are derived for the optimal estimating functions when the classes of generalized prediction-based estimating functions are defined by a finite-dimensional space of predictors. Only unconditional moments are needed for this class of estimating functions, so a considerably smaller amount of simulation is needed compared to other classes of estimating functions based on conditional moments. Particular attention is devoted to the Cox-Ingersoll-Ross model and stochastic volatility models. Using Monte Carlo simulation the small-sample properties are examined and the method is compared to other estimating functions. Keywords: Martingale estimating functions, Monte Carlo simulation, nonlinear filtering, prediction-based estimating functions, stochastic volatility models, stochastic differential equations.

JEL classification: C13

Mathematics Subject Classification (1991): 62M20, 62P05, 93E11

IMM technical report 10/2000

Last update 26-5-2000 by fkc
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