  Financial econometrics has become an increasingly popular research field. In
this paper we review a few parametric and nonparametric models and methods used
in this area. After introducing several widely used continuous-time and
discrete-time models, we study in detail dependence structures of discrete
samples, including Markovian property, hidden Markovian structure, contaminated
observations, and random samples. We then discuss several popular parametric
and nonparametric estimation methods. To avoid model mis-specification, model
validation plays a key role in financial modeling. We discuss several model
validation techniques, including pseudo-likelihood ratio test, nonparametric
curve regression based test, residuals based test, generalized likelihood ratio
test, simultaneous confidence band construction, and density based test.
Finally, we briefly touch on tools for studying large sample properties.
