Inference in stochastic volatility models for Gaussian and t data

Two competing analytical approaches, namely, the generalized method of moments (GMM) and quasi-maximum likelihood (QML) are widely used in statistics and econometrics literature for inferences in stochastic volatility models (SVMs). Alternative numerical approaches such as Markov chain Monte Carlo (MCMC), simulated maximum likelihood (SML) and Bayesian approaches are also available. All these later approaches are, however, based on simulations. Tagore (2010) revisited the analytical estimation approaches and proposed simpler and more efficient method of moments (MM) and approximate GQL (AGQL) inferences for the estimation of the volatility parameters. However, Tagore (2010) did not consider the estimation of the intercept parameter (γ0) in the SV model, and also the model was confined to the normal based errors only. -- In this thesis, we first extend Tagore's MM and AGQL approaches (Tagore 2010) to the estimation of all parameters of the SV model including the so-called intercept parameter γ0. Second, we modify the existing QML approach and unlike Tagore (2010) include this approach in the simulation study. Furthermore, all three approaches are applied to analyze a real life dataset. -- Next, we consider a t-distribution based SV model, and apply the aforementioned estimation approaches for all parameters including a new degrees of freedom parameter of the t-distribution. Simulation studies are conducted to examine the relative performances of the estimation approaches. We also compute the kurtosis of the t-distribution based SV models and make an exact comparison with those of normal distribution based SV models. The estimation effect of parameters on the kurtosis is given for a special case