这篇论文研究了当假设的数据分布与实际不符时估计多维乘积误差模型参数的方法，和该模型在预测领域的应用。论文的第一部分讨论了两种在以前的文献中被用来估计该模型的估计方法：最大似然估计法和广义矩估计法。并在对数据做了不同的干扰后比较了这两种方法。比较结果显示这两种方法都易受偏离值的影响。因此论文的第二部分提出了一种新的估计方法：权重经验似然估计法。在模拟实验和使用包含了当前经济危机间断数据的标准普尔指数的实际实验中，对比最大似然估计法和广义矩估计法，权重经验似然函数显示出了对偏离值有更好的抗性。论文的第三部分进一步研究了多维乘积误差模型在预测中的应用。并且这一部分还提出了实波动性的一种新的分解方式。分解得到的两个新的变量可以被多维乘积误差模型所模拟。通过比较标准普尔指数和纳斯达克指数的预测结果，比起以前用来估计实波动性的三种模型，多维乘积向量模型和新的分解方式显示出了更强的预测能力。 / This thesis studies the estimations of vector Multiplicative Error Model (MEM) under different kinds of model mismatches and its application in forecasting. In the first part of the thesis, two estimation methods, Maximum Likelihood (ML) method and Generalized Method of Moments (GMM), which have previously been used on vector MEM, are compared through different situations of data contaminations. From the comparison results it is found that both ML and GMM estimators are suspected to outliers in data. Therefore in the second part of the thesis a novel estimator is proposed: Weighted Empirical Likelihood (WEL) estimator. It is shown to be more robust than ML and GMM estimators in simulations, and also in forecasting realized volatility and bipower volatility of S&P 500 stock index including the current financial crisis period. The forecast ability of vector MEM is further addressed in the third part of the thesis, where an alternative decomposition of realized volatility is proposed, and vector MEM is used to model and forecast the two components of realized volatility. From the realized volatility forecasts of S&P 500, NASDAQ and Dow Jones, this decomposition together with vector MEM are illustrated to have superior performances over three competing models which have been applied on forecasting realized volatility before. / Detailed summary in vernacular field only. / Ding, Hao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 203-213). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Outline of the thesis --- p.5 / Chapter 1.2 --- Conclusion --- p.7 / Chapter 2 --- Background study --- p.9 / Chapter 2.1 --- Multiplicative Error Model --- p.9 / Chapter 2.1.1 --- Introduction --- p.9 / Chapter 2.1.2 --- Developments of MEM --- p.12 / Chapter 2.1.3 --- Vector MEM --- p.17 / Chapter 2.2 --- Two functions for multivariate analysis --- p.25 / Chapter 2.2.1 --- Copula function --- p.25 / Chapter 2.2.2 --- Depth function --- p.32 / Chapter 3 --- Two Estimators for Vector MEM --- p.39 / Chapter 3.1 --- Two Stage Maximum Likelihood --- p.40 / Chapter 3.1.1 --- Introduction --- p.41 / Chapter 3.1.2 --- Simulation of two stage ML --- p.44 / Chapter 3.2 --- Maximum Likelihood estimator --- p.48 / Chapter 3.2.1 --- Derivatives of score function --- p.50 / Chapter 3.3 --- GMM estimator --- p.57 / Chapter 3.4 --- Comparing ML and GMM through simulations --- p.60 / Chapter 3.4.1 --- Generation of clean data --- p.61 / Chapter 3.4.2 --- Data contamination --- p.62 / Chapter 3.4.3 --- Optimization --- p.64 / Chapter 3.4.4 --- Resutls on clean data --- p.65 / Chapter 3.4.5 --- Results on contaminated data --- p.66 / Chapter 3.5 --- conclusion --- p.69 / Chapter 4 --- Weighted Empirical Likelihood Estimator --- p.77 / Chapter 4.1 --- Introduction --- p.78 / Chapter 4.2 --- Vector multiplicative error model and two estimation methods --- p.83 / Chapter 4.3 --- Weighted Empirical Likelihood --- p.88 / Chapter 4.3.1 --- Inner optimization --- p.93 / Chapter 4.3.2 --- Calculation of weights --- p.97 / Chapter 4.4 --- Simulation study on outliers --- p.101 / Chapter 4.4.1 --- Clean data --- p.103 / Chapter 4.4.2 --- Outliers --- p.105 / Chapter 4.4.3 --- Simulation results --- p.108 / Chapter 4.5 --- Computations of high dimension vector MEM --- p.111 / Chapter 4.5.1 --- The influences of dimension on ML --- p.111 / Chapter 4.5.2 --- The influences of dimension on GMM --- p.113 / Chapter 4.5.3 --- The influences of dimension on WEL --- p.115 / Chapter 4.5.4 --- Simulation --- p.116 / Chapter 4.6 --- Compare weighted empirical likelihood and empirical likelihood --- p.118 / Chapter 4.7 --- Empirical example --- p.121 / Chapter 4.7.1 --- Model --- p.123 / Chapter 4.7.2 --- Forecast comparison criteria --- p.125 / Chapter 4.7.3 --- Results --- p.126 / Chapter 4.8 --- Conclusions --- p.127 / Chapter 5 --- Forecast RV by Vector MEM --- p.142 / Chapter 5.1 --- Introduction --- p.143 / Chapter 5.2 --- Multiplicative jump and vector MEM --- p.148 / Chapter 5.2.1 --- Multiplicative jump --- p.148 / Chapter 5.2.2 --- Vector MEM for jump and continuous components --- p.153 / Chapter 5.3 --- Empirical analysis --- p.156 / Chapter 5.3.1 --- Data summary --- p.157 / Chapter 5.3.2 --- Models --- p.160 / Chapter 5.3.3 --- Forecast comparison criteria --- p.164 / Chapter 5.3.4 --- Before-crisis period --- p.166 / Chapter 5.3.5 --- Crisis period --- p.172 / Chapter 5.3.6 --- Comparing M-jump and log M-jump --- p.176 / Chapter 5.3.7 --- Conclusion on empirical analysis --- p.183 / Chapter 5.4 --- Conclusion --- p.185 / Chapter 6 --- Conclusion and future Work --- p.198 / Bibliography --- p.203
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328015 |
| Date | January 2013 |
| Contributors | Ding, Hao, Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xv, 213 leaves) : ill. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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