Modeling conditional heteroskedasticity in time series and spatial analysis

My dissertation consists of three separate chapters. In the first chapter I introduce semiparametric modeling of dependent data using estimating function approach. Once aim of this chapter is to provide an account of the developments relating to the theory of estimating functions. Starting from the simple case of a single parameter under independence, I cover the multiparameter, presence of nuisance parameters and dependent data cases.; In the second chapter, I propose modeling equity volatilities as a combination of higher moment effects and time series dynamics. This paper extends the existing literature in the direction of robust characterization on the nature of relation between conditional mean and conditional variance of the excess stock returns using GARCH class of models. In order to estimate model parameters I combine two estimating functions which are unbiased, orthogonal to each other and have both skewness and excess kurtosis in their arguments. The semiparametric nature of the model helps to avoid misspecification relating to the underlying density function. The simulation analysis shows the finite sample properties of the optimal EF estimators. Empirical illustration using daily and monthly index and equity returns data demonstrates the usefulness of our suggested procedures.; My fourth chapter investigates heterogeneity in the assessment of spatial dependence by exploring (jointly) two main mechanisms: distributional misspecification and conditional heteroskedasticity. I first derive a simple specification test for spatial autoregressive model using the information matrix (IM) test principle. As a byproduct of my test development, I obtain a general model that has similar features like autoregressive conditional heteroskedasticity (ARCH) in time series context. My suggested spatial ARCH (SARCH) model can take account of some of the stylized facts observed in spatial data. To illustrate the usefulness of our test and SARCH model, I apply our theoretical result to Boston housing price data and show the importance of modeling the conditional second moment in spatial context.