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Parametric and nonparametric models and methods in financial econometrics

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Author(s): Zhibiao Zhao

Journal: Statistics Surveys
ISSN 1935-7516

Volume: 2;
Start page: 1;
Date: 2008;
Original page

Keywords: Diffusion model | Hidden Markov model | Jump diffusion model | Markov chain | Model validation | Nonlinear time series | Nonparametric density estimate | Nonparametric curve estimate | Stochastic differential equation | Stochastic volatility

ABSTRACT
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.
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