The analysis and prediction of diffusion processes
plays a fundamental role in the statistical analysis of
financial markets.
The techniques applied rely on the actual model
assumed for the drift and diffusion coefficient functions.
Mismodelling these coefficients might result in biased prediction and
incorrect parameter specification.
We show in this chapter
how the empirical likelihood technique,
Owen (1988) and Owen (1990),
may be used to construct test procedures for
the Goodness-of-Fit of a diffusion model.
The technique is based on comparison with kernel smoothing estimators.
The Goodness-of-Fit test proposed is based on the asymptotics of the
empirical likelihood, which has two attractive features. One is its
automatic consideration of the variation associated with the
nonparametric fit due to the empirical likelihood's
ability to studentize internally. The other one is that
the asymptotic distributions
of the test statistic are free of unknown parameters which
avoids secondary plug-in estimation.