An Empirical Likelihood Goodness-of-Fit Test for Diffusions
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 likeUhood, 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.
KeywordsStochastic Differential Equation Empirical Likelihood Kernel Estimator Stock Market Index Empirical Likelihood Method
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