Multivariate GARCH models using copula, nonparametric and semiparametric methods.

详细信息   

• 作者：Long ; Xiangdong.
• 学历：Doctor
• 年：2005
• 导师：Lee, Tae-Hwy
• 毕业院校：University of California
• 专业：Economics, General.;Economics, Finance.
• ISBN：0542345714
• CBH：3191675
• Country：USA
• 语种：English
• FileSize：4313186
• Pages：104

文摘

My dissertation is consistent of two chapters. In Chapter 1, for non-elliptically distributed financial returns, I propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of two dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests the conventional MGARCH models as special cases in the case of elliptical distributions. I apply this idea to the three benchmark models, namely, the dynamic conditional correlation model of Engle (2002), the varying correlation model of Tse and Tsui (2002) and the scalar BEKK model of Engle and Kroner (1995). Monte Carlo simulation illustrates the effect of density misspecifications via the log-likelihood function and l 2-matrix norm. Comparing the in-sample model selection criteria and the out-of-sample predictive ability, we find that the C-MGARCH models outperform the benchmark models when these models are applied to pairs of the foreign exchange rates and the U.S. equity indices. Both the in-sample estimation results and the out-of-sample forecasting results are clearly in favor of our new models.;In Chapter 2, I propose two nonparametric MGARCH (NMGARCH) models: the Cholesky Factorization and the Nadaraya-Watson estimation. Both can guarantee the positive definite of the conditional covariance matrix estimator and the former degenerates to the later under some circumstances. These methodologies could also be applied to capture the information hidden in the standardized errors missed by the parametric MGARCH models. Our two-stage semiparametric MGARCH (SMGARCH) model firstly estimates parametric MGARCH model, then use the nonparametric skills to model the conditional covariance matrix of the standardized errors, finally incorporates multiplicatively both parametric and nonparametric estimators of two stages together to get the conditional covariance matrix of the interested variables. Three Monte Carlo simulation experiments demonstrate the advantages of NMGARCH and SMGARCH in terms of statistical loss functions and economic loss function. Our models outperform the parametric MGARCH models in the empirical applications on stock indexes and foreign exchange rates. The superiority of semiparametric methodology over nonparametric modeling is also clearly.