Three essays on econometrics: Asymmetric exponential power distribution, econometric computation, and multifactor model

The dissertation consists of three independent essays, and they are put in as three chapters.;The goal of the first chapter is to develop an estimation procedure for financial time series models with the error terms following the Asymmetric Exponential Power Distribution (AEPD). The AEPD is the most general class of unimodal distributions. In addition to the usual location and scale parameters, it has skewness and kurtosis parameters. The kurtosis parameter is hard to estimate when the sample size is small and skewness is large. We show that when the skewness parameter is either close to zero or close to one the estimation of the kurtosis parameters are virtually unidentifiable unless the sample size is large. We analyze the nonlinear GARCH model (NGARCH) and an asset pricing model known as CKLS. We devise Bayesian Markov chain Monte Carlo (MCMC) algorithms.;In chapter 2, we focus on econometric computation and develop a method to speed up intensive computation. The combination of MATLAB, C/C++ and Graphic Processing Unit (GPU) is a method to put convenience and speed together. MATLAB is a high level computing language for econometrics. C/C++ language, on the other hand, is more flexible and more powerful than interpreted languages such as GAUSS, MATLAB and SAS. But it requires more professional programming skills. There are three levels of speedup (within one personal computer). The lowest is simple C++ substitution. The faster level is parallel computing using multicore CPU. The fastest speed-up is parallel computing using GPU cards. The compiled codes which use GPU can run in MATLAB hundreds time faster than corresponding MATLAB script functions.;In chapter 3, we focus on the estimation of the multifactor CKLS model. The CKLS model provides a simple econometric framework to nest some popular term structure models such as the ones proposed by Merton (1973), Vasicek (1977), and Cox, Ingasol and Ross (CIR) (1985). In this chapter, we provide a new MCMC algorithm to estimate the multifactor CKLS model. Compared to the algorithm in Sowar (2005), our algorithm is more efficient and can be applied to multifactor models whose dimension is more than two.