Testing for One Factor Models versus Stochastic Volatility Models, in the Presence of Jumps.∗

This paper provides a testing procedure which allows to discriminate between one factor and stochastic volatility models, under minimal assumptions. In particular, apart from standard regularity conditions, no assumptions are made on the functional forms of either the drift or the variance term. The suggested test statistic can be seen as an Hausman type test. In fact, our test is constructed by comparing two estimators of integrated volatility: one is a kernel estimator of the instantaneous variance, averaged over the sample realization on a fixed time span; the other is realized volatility. Under the null hypothesis of a one factor model, both estimators are consistent for the “true ” integrated volatility, but the former is more efficient. Under the alternative hypothesis, the kernel type estimator is not consistent, while realized volatility retains the consistency property. A version of the test which is robust to the presence