Browsing by Author "Huang, Chun-Kai."
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Item Modeling financial data using the multivariate generalized hyperbolic distribution and copula.(2015) Kemda, Lionel Establet.; Chinhamu, Knowledge.; Huang, Chun-Kai.Financial data usually possess some characteristics, such as volatility clustering, asymmetry, heavy and semi-heavy tails thus, making it difficult, if not impossible, to use Normal distribution to model them. Statistical analyzis shows that the Generalized hyperbolic distribution is appropriate for capturing these characteristics. This research shows that the USD/ZAR, All shares, Gold mining as well as the the S&P 500 returns are best modeled with the Skew t, generalized hyperbolic, hyperbolic, generalized hyperbolic distributions respectively based on AIC and Value-at-Risk (VAR) backtesting. Further multivariate analyzis of these returns based on the kernel smoothing goodness of fit shows that; the multivariate affine normal inverse gaussian (MANIG) distribution provides the best fit for the affine models. Likewise, the multivariate normal inverse gaussian (MNIG) distribution based on AIC provides the best model for the four returns. Finally, the positive tail dependencies exhibited between the All shares and Gold mining returns as well as All shares and S&P 500 returns is best modeled with the Gumbel and Clayton copulas respectively. While the negative dependencies between the USD/ZAR returns and other returns is modeled with the Frank copula.Item Special topics in probabilistic exchangeability and its applications.(2017) Huang, Chun-Kai.; North, Delia Elizabeth.; Zewotir, Temesgen Tenaw.This thesis evolves around a probabilistic concept called exchangeability and its generalised forms. It is aimed at exploring connections between exchangeability and other sub-areas in mathematical statistics. These connections include theoretical implications, generalisation of existing methodologies and applications to real-world data. There are three topics of particular interest. The rst topic is related to the linkage between de Finetti's representation theorem (for exchangeable sequences) and existence conditions for Hausdor moment problems over k-dimensional simplexes. The equivalence of these two results are proved over the most general case in nite spaces. This is a generalisation of existing theory and uses an alternative approach to previous work in the literature. This connection, while theoretically interesting in its own right, may also lead to further cross- eld applications, such as distribution re-construction from nite moments or in the approximations to nite exchangeable sequences and nite moment problems. Secondly, we explore a currently popular topic, namely extreme value theory (EVT), which has been widely applied to areas such as hydrology, earth sciences and nance. Classical results from EVT assume that the data sequence is independent and identically distributed (IID). We generalise this assumption to exchangeable random sequences. This caters for more general approaches to EVT that allows for data dependency. Resampling techniques are utilised for estimating the parameters' prior distributions. We utilise these new methods for Value-at-Risk (VaR) estimation in nancial stock returns. This is done for both cases with and without GARCH lters. These new VaR models are also compared to existing models in the literature and shows promising improvements. For the nal topic, exchangeability is applied to two-phase sampling with an auxiliary variable. In particular, our focus is on a two-phase strati ed sampling design, under the assumption that readings for the study variable are exchangeable within stratum. This will again provide a generalisation from the usual IID assumption in applications of multiple-phase sampling. It is amalgamated with stationary bootstrapping at various levels of sampling to estimate within stratum and cross strata covariances. We show that our approach provides a more conservative estimate for the sampling variance of the two-phase estimator for the mean (i.e., the ratio estimator), as compared to the conventional IID method by Rao (1973)