Discrete- and continuous-time stochastic volatility (SV) models are introduced to explain
conditional heterogeneity and dependence along with conditional leptokurtosis found in higher order
moments of two stock market index return processes. We use the efficient method of moments
(EMM) procedure combined with the seminonparametric (SNP) model as the score generator to
estimate SV models. The EMM is applicable to a variety of asset pricing models where the moment
restrictions contain unobservable state vector and improves efficiency of the estimator without
resorting to the likelihood approach. By employing EMM in estimating two SV models with SNP
auxiliary models, we aim to evaluate the performance of the SNP conditional density function and
the SV models in characterizing non-Gaussianity of the conditional volatility process. As seen
from the empirical results, the SV models fail to fit the various scores considered in the EMM
estimation. The SV models are not appropriate for capturing the characteristics of non-Gaussianity,
fat-tailed behavior and conditional heterogeneity of the observed data. We also find that the SNP
models are more appropriate in modeling non-Gaussianity and non-linear dynamics along with
conditional heterogeneity of the conditional distribution in the index return process.
Keywords：Efficient Method of Moments, Seminonparametric Methods, Hermite Expansion,
Non-Gaussianity, Conditional Heterogeneity, Stochastic Volatility