Tang Him John. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 76-80). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgment --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.2 / Chapter 1.1.1 --- Linear Time Series --- p.2 / Chapter 1.1.2 --- Mixture Models --- p.3 / Chapter 1.1.3 --- EM algorithm --- p.6 / Chapter 1.1.4 --- Model Selection --- p.6 / Chapter 1.2 --- Main Objectives --- p.7 / Chapter 1.3 --- Outline of this thesis --- p.7 / Chapter 2 --- Finite Gaussian Mixture ARMA-GARCH Model --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.1.1 --- "AR, MA, and ARMA" --- p.10 / Chapter 2.1.2 --- Stationarity --- p.11 / Chapter 2.1.3 --- ARCH and GARCH --- p.12 / Chapter 2.1.4 --- Gaussian mixture --- p.13 / Chapter 2.1.5 --- EM and GEM algorithms --- p.14 / Chapter 2.2 --- Finite Gaussian Mixture ARMA-GARCH Model --- p.16 / Chapter 2.3 --- Estimation of Gaussian mixture ARMA-GARCH model --- p.17 / Chapter 2.3.1 --- Autocorrelation and Stationarity --- p.20 / Chapter 2.3.2 --- Model Selection --- p.24 / Chapter 2.4 --- Experiments: First Step Prediction --- p.26 / Chapter 2.5 --- Chapter Summary --- p.28 / Chapter 2.6 --- Notations and Terminologies --- p.30 / Chapter 2.6.1 --- White Noise Time Series --- p.30 / Chapter 2.6.2 --- Lag Operator --- p.30 / Chapter 2.6.3 --- Covariance Stationarity --- p.31 / Chapter 2.6.4 --- Wold's Theorem --- p.31 / Chapter 2.6.5 --- Multivariate Gaussian Density function --- p.32 / Chapter 3 --- Finite Mixture-of-Expert ARMA-GARCH Model --- p.33 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.1.1 --- Mixture-of-Expert --- p.34 / Chapter 3.1.2 --- Alternative Mixture-of-Expert --- p.35 / Chapter 3.2 --- ARMA-GARCH Finite Mixture-of-Expert Model --- p.36 / Chapter 3.3 --- Estimation of Mixture-of-Expert ARMA-GARCH Model --- p.37 / Chapter 3.3.1 --- Model Selection --- p.38 / Chapter 3.4 --- Experiments: First Step Prediction --- p.41 / Chapter 3.5 --- Second Step and Third Step Prediction --- p.44 / Chapter 3.5.1 --- Calculating Second Step Prediction --- p.44 / Chapter 3.5.2 --- Calculating Third Step Prediction --- p.45 / Chapter 3.5.3 --- Experiments: Second Step and Third Step Prediction . --- p.46 / Chapter 3.6 --- Comparison with Other Models --- p.50 / Chapter 3.7 --- Chapter Summary --- p.57 / Chapter 4 --- Stable Estimation Algorithms --- p.58 / Chapter 4.1 --- Stable AR(1) estimation algorithm --- p.59 / Chapter 4.2 --- Stable AR(2) Estimation Algorithm --- p.60 / Chapter 4.2.1 --- Real p1 and p2 --- p.61 / Chapter 4.2.2 --- Complex p1 and p2 --- p.61 / Chapter 4.2.3 --- Experiments for AR(2) --- p.63 / Chapter 4.3 --- Experiment with Real Data --- p.64 / Chapter 4.4 --- Chapter Summary --- p.65 / Chapter 5 --- Conclusion --- p.66 / Chapter 5.1 --- Further Research --- p.69 / Chapter A --- Equation Derivation --- p.70 / Chapter A.1 --- First Derivatives for Gaussian Mixture ARMA-GARCH Esti- mation --- p.70 / Chapter A.2 --- First Derivatives for Mixture-of-Expert ARMA-GARCH Esti- mation --- p.71 / Chapter A.3 --- First Derivatives for BYY Harmony Function --- p.72 / Chapter A.4 --- First Derivatives for stable estimation algorithms --- p.73 / Chapter A.4.1 --- AR(1) --- p.74 / Chapter A.4.2 --- AR(2) --- p.74 / Bibliography --- p.80
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324391 |
| Date | January 2003 |
| Contributors | Tang, Him John., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xi, 80 leaves : ill. ; 30 cm. |
| 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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