Yick, Kwok Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 67-68). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The importance of forecasting --- p.1 / Chapter 1.2 --- Objective --- p.3 / Chapter 2 --- Vector Autoregressive Model --- p.5 / Chapter 2.1 --- The VAR(p) model --- p.5 / Chapter 2.2 --- Least squares estimation method --- p.7 / Chapter 2.3 --- VAR order selection method --- p.10 / Chapter 2.4 --- Constructing simultaneous prediction intervals procedures --- p.11 / Chapter 2.4.1 --- Bonferroni procedure --- p.12 / Chapter 2.4.2 --- The 'Exact' procedure --- p.13 / Chapter 2.4.3 --- Two variables case --- p.15 / Chapter 2.4.4 --- Three variables case --- p.18 / Chapter 3 --- A System of Linear Equations with Exogenous Variables --- p.23 / Chapter 3.1 --- Restriction of VAR model --- p.23 / Chapter 3.2 --- Least squares estimation method --- p.24 / Chapter 3.3 --- Hsiao's sequential method for estimating the lag lengths --- p.26 / Chapter 3.3.1 --- Two variables case --- p.27 / Chapter 3.3.2 --- Three variables case --- p.29 / Chapter 3.4 --- Using VAR model to construct simultaneous prediction intervals --- p.32 / Chapter 3.4.1 --- Bonferroni procedure --- p.34 / Chapter 3.4.2 --- The 'Exact' procedure --- p.35 / Chapter 3.4.3 --- Two variables case --- p.36 / Chapter 3.4.4 --- Three variables case --- p.38 / Chapter 4 --- Illustrative Examples --- p.42 / Chapter 5 --- A Simulation Study --- p.52 / Chapter 5.1 --- Design of the experiment --- p.52 / Chapter 5.2 --- Simulation results --- p.58 / Chapter 5.3 --- Concluding remarks --- p.60 / Chapter 5.4 --- Further research --- p.60 / References --- p.67

時間序列之變點鬥檻模型是一種非線性的模型。此論文探討有關該模型之參數估計，同時對其參數估計作出統計分析。我們運用了遺傳式計算機運算來估計這些參數及對其作出研究。我們利用了MDL來對比不同的變點門檻模型，同時我們也利用了MDL來選取對應的變點門檻模型。 / This article considers the problem of modeling non-linear time series by using piece-wise TAR model. The numbers of change points, the numbers of thresholds and the corresponding order of AR in each piecewise TAR segments are assumed unknown. The goal is to nd out the “best“ combination of the number of change points, the value of threshold in each time segment, and the underlying AR order for each threshold regime. A genetic algorithm is implemented to solve this optimization problem and the minimum description length principle is applied to compare various segmented TAR. We also show the consistency of the minimal MDL model selection procedure under general regularity conditions on the likelihood function. / Detailed summary in vernacular field only. / Tang, Chong Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 45-47). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 2 --- Minimum Description Length for Pure TAR --- p.4 / Chapter 2.1 --- Model selection using Minimum Description Length for Pure TAR --- p.4 / Chapter 2.1.1 --- Derivation of Minimum Description Length for Pure TAR --- p.5 / Chapter 2.2 --- Optimization Using Genetic Algorithms (GA) --- p.7 / Chapter 2.2.1 --- General Description --- p.7 / Chapter 2.2.2 --- Implementation Details --- p.9 / Chapter 3 --- Minimum Description Length for TAR models with structural change --- p.13 / Chapter 3.1 --- Model selection using Minimum Description Length for TAR models with structural change --- p.13 / Chapter 3.1.1 --- Derivation of Minimum Description Length for TAR models with structural change --- p.14 / Chapter 3.2 --- Optimization Using Genetic Algorithms --- p.17 / Chapter 4 --- Main Result --- p.20 / Chapter 4.1 --- Main results --- p.20 / Chapter 4.1.1 --- Model Selection using minimum description length --- p.21 / Chapter 5 --- Simulation Result --- p.24 / Chapter 5.1 --- Simulation results --- p.24 / Chapter 5.1.1 --- Example of TAR Model Without Structural Break --- p.24 / Chapter 5.1.2 --- Example of TAR Model With Structural Break I --- p.26 / Chapter 5.1.3 --- Example of TAR Model With Structural Break II --- p.29 / Chapter 6 --- An empirical example --- p.33 / Chapter 6.1 --- An empirical example --- p.33 / Chapter 7 --- Consistency of the CLSE --- p.36 / Chapter 7.1 --- Consistency of the TAR parameters --- p.36 / Chapter 7.1.1 --- Consistency of the estimation of number of threshold --- p.36 / Chapter 7.1.2 --- Consistency of the change point parameters --- p.43 / Bibliography --- p.45

門限協整是金融和統計研究中一個充滿活力的課題。其估計方法往往基於向量誤差修正模型，并儘限於單門限情形。本論文研究了多門限協整模型的估計問題。針對多門限協整，我們提出了兩種基於多門限向量誤差修正模型的估計方法：最小二乘估計和光滑最小二乘估計，并給出了最小二乘估計的收斂速度和建立了光滑最小二乘估計的極限分佈。爲了對這兩種估計方法的性能進行評估，我們展開了一項模擬實驗，實驗結果印證了本文給出的極限理論。通過多門限協整模型，我們隊利率期限結構進行了研究。 / 最後，本論文研究了光滑轉移協整的最小二乘估計方法，并給出了其極限分佈。 / Threshold cointegration has been a vibrant research topic in finance and statistics. Estimation procedures of threshold cointegrated models are usually based on the so-called threshold vector error correction forms (TVECMs) for one threshold case. In this thesis, we investigate two estimators for multiple thresholds cointegrations via TVECMs, namely the least squares estimator and the smoothed least squares estimator. The convergence rate of the least squares estimator is obtained and limiting distribution of the smoothed least squares estimator is developed. To assess the performance of these two estimators, we conduct a simulation study, the result of which supports the asymptotic theories developed. We study the term structure of interest rates by a two thresholds cointegration as an example. / Finally we also investigate the least squares estimator of smooth transition cointegration and establish the limiting distribution. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Man. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 83-88). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Two-step Estimator --- p.3 / Chapter 1.1.2 --- Simultaneous Estimator --- p.4 / Chapter 1.2 --- Outline --- p.6 / Chapter 2 --- Threshold Cointegration --- p.7 / Chapter 2.1 --- Linear Cointegration --- p.7 / Chapter 2.1.1 --- Representation --- p.9 / Chapter 2.1.2 --- Two-step Estimator --- p.10 / Chapter 2.2 --- Threshold Cointegration --- p.12 / Chapter 2.2.1 --- SETAR Representation and Estimation --- p.12 / Chapter 2.2.2 --- TVECM Representation and Estimation --- p.15 / Chapter 3 --- LSE of Multipe Thresholds Cointegration --- p.17 / Chapter 3.1 --- Multipe Thresholds Cointegration --- p.17 / Chapter 3.2 --- TVECM Representation and LSE --- p.18 / Chapter 3.3 --- Assumptions and Results --- p.20 / Chapter 4 --- SLSE of Multiple Thresholds Cointegration --- p.25 / Chapter 4.1 --- Smoothed LSE (SLSE) --- p.25 / Chapter 4.2 --- TVECM and Estimation --- p.27 / Chapter 4.3 --- Assumptions and Results --- p.29 / Chapter 4.4 --- Asymptotic Variance --- p.34 / Chapter 5 --- Simulation and Empirical Studies --- p.38 / Chapter 5.1 --- Simulation Study --- p.38 / Chapter 5.1.1 --- Experiment Design --- p.38 / Chapter 5.1.2 --- Simulation Results --- p.40 / Chapter 5.2 --- Term Structure of Interest Rates --- p.42 / Chapter 6 --- Smooth Transition Cointegration --- p.50 / Chapter 6.1 --- Smooth Transition Cointegration --- p.51 / Chapter 6.2 --- Assumptions and Results --- p.52 / Chapter 7 --- Conclusion and Further Research --- p.56 / Chapter 7.1 --- Conclusion --- p.56 / Chapter 7.2 --- Future Research --- p.59 / Chapter 7.2.1 --- Nested Testing --- p.59 / Chapter 7.2.2 --- Limiting Distribution of LSE --- p.60 / Chapter 7.2.3 --- Other Nonlinear Cointegration --- p.60 / Chapter A --- Technical Proofs --- p.63 / Chapter B --- Some Formulas --- p.82 / Bibliography --- p.83

Then, we consider the patterns between news stream and time series indices stream. We first transform the news stream into a set of bursty feature (keywords) time series streams and propose three technique to study their relationship to time series index. First, we explore a Non-homogeneous Hidden Markov Model (NHMM) to predict the stock market process which takes both stock prices and news articles into consideration. Second, we propose a risk analytical model to predict the volatility of price indices by integrating news information. Finally, we devise an algorithm to detect the priming event from text and a time series index. The evaluation on real world dataset suggests the significant correlation exists between news stream and time series stream and our pattern discover algorithm can detect promising patterns from this relationship to support real world applications effectively. / We start from investigating the co-movement relationship of multiple time series. We propose techniques to study two aspects of this problem. First, we propose a co-movement model for constructing financial portfolio by analyzing and mining the co-movement patterns among two time series. Second, we presents an efficient streaming algorithm to discover leaders from multiple time series stream. Both of the algorithms are evaluated using real time series indices data and the result proves that co-movement patterns and detected leaders are promising and can support various applications including portfolio management, high frequency trading and risk management. / With the increasing amount of data in financial market, there are two types of data streams attracting a lot of research and studies, time series index stream and related news stream. In this thesis, we focus on discovering patterns from these data streams and try to answer the following challenging questions, (I) given two co-evolving time series indices, what is the co-movement dependency between them. (II) given a set of evolving time series, could we detect some leaders from them whose rise or fall impacts the behavior of many other time series? (III) could we integrate the news stream information into stock price prediction? (IV) could we integrate the news stream information into stock risk analysis? and (V) could we detect what are those events that trigger time series index movement. For each of the question, we design algorithms and address three technique issues (I) how to detect promising patterns from the noisy financial data; (II) how to update the old patterns when new data arrives in high frequency; (III) how to use the pattern to support the financial applications. / Wu, Di. / Adviser: Jeffrey Xu Pu. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 124-131). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The first part of this thesis considers the residual empirical process of a nearly unstable long-memory time series. Chan and Ling [8] showed that the usual limit distribution of the Kolmogorov-Smirnov test statistics does not hold when the characteristic polynomial of the unstable autoregressive model has a unit root. A key question of interest is what happens when this model has a near unit root, that is, when it is nearly non-stationary. In this thesis, it is established that the statistics proposed by Chan and Ling can be extended. The limit distribution is expressed as a functional of an Orenstein-Uhlenbeck process that is driven by a fractional Brownian motion. This result extends and generalizes Chan and Ling's results to a nearly non-stationary long-memory time series. / The second part of the thesis investigates the weak convergence of weighted sums of random variables that are functionals of moving aver- age processes. A non-central limit theorem is established in which the Wiener integrals with respect to the Hermite processes appear as the limit. As an application of the non-central limit theorem, we examine the asymptotic theory of least squares estimators (LSE) for a nearly unstable AR(1) model when the innovation sequences are functionals of moving average processes. It is shown that the limit distribution of the LSE appears as functionals of the Ornstein-Uhlenbeck processes driven by Hermite processes. / Liu, Weiwei. / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 60-67). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

by Xin-xin Niu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

A major objective of this thesis is to study the statistical inference problem for GARCH-type models, including fractionally-integrated (FI) GARCH, fractional (F) GARCH, long-memory (LM) GARCH, and non-stationary GARCH models. / Among various types of generalizations to the ARCH models, fractionally-integrated (FI) GARCH model proposed in Baillie et al. (1996) and Bollerslev and Mikkelson (1996) is one of the most interesting ones as it offered many challenging theretical problems. / Parameters in the ARCH-type models are commonly estimated using the quasi-maximum likelihood estimator (QMLE). To establish consistency and asymptotic normality of the QMLE, one usually has to impose stringent assumptions, see Robinson and Zaffaroni (2006) and Straumann (2005). They have to assume that a stationary solution to the true model exists and this solution has some finite moments. These two assumptions are too restrictive to be applied to FIGARCH models. Formal results of the asymptotic properties of the QMLE of the FIGARCH models are still not available. Progresses on asymptotic theory of QMLE have only been made on certain models that resemble the FIGARCH model, including the FGARCH model of Ding and Granger (1996) and Robinson and Zaffaroni (2006), the LM-GARCH model of Robinson and Zaffaroni (1997) and the non-stationary ARCH model, but not the FIGARCH model itself. / This study attempts to solve the FIGARCH problem and extend the current findings on FGARCH, LM-GARCH and non-stationary GARCH models. We show that if the fractional parameter d is known, the QMLE for the parameters are strongly consistent and asymptotically normal. The results of LM-GARCH (0, d, 0) model in Konlikov (2003a,b) will be generalized to encompass the LM-GARCH(p, d, q) models. We also furnish a general result for non-stationary GARCH (p, q) models, extending the results of Jensen and Rahbek (2004) on weak consistency and asymptotic normality of the QMLE of the non-stationary GARCH (1, 1) models. / Ng, Chi Tim. / "June 2007." / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0398. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Wan Po Man Polly. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 122-128). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.v / Contents --- p.vi / List of Figures --- p.x / List of Tables --- p.xiv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation and Aims --- p.1 / Chapter 1.2 --- Organization of Thesis --- p.5 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Dimensionality Reduction --- p.6 / Chapter 2.1.1 --- Fourier Transformation --- p.6 / Chapter 2.1.2 --- Wavelet Transformation --- p.8 / Chapter 2.1.3 --- Singular Value Decomposition --- p.10 / Chapter 2.2 --- Searching Sequence Similarity with Transformation --- p.11 / Chapter 2.2.1 --- Time Warping --- p.11 / Chapter 2.2.2 --- Amplitude Scaling and Shifting --- p.14 / Chapter 2.3 --- Data Smoothing and Noise Removal --- p.18 / Chapter 2.3.1 --- Piecewise Linear Segmentations --- p.18 / Chapter 2.3.2 --- Approximation Function --- p.21 / Chapter 2.3.3 --- Best-fitting Line --- p.23 / Chapter 2.3.4 --- Turning Points --- p.24 / Chapter 3 --- Time-Series Searching with Scaling and Shifting in Amplitude and Time Domains --- p.25 / Chapter 3.1 --- Representation --- p.25 / Chapter 3.1.1 --- Control Points --- p.26 / Chapter 3.1.2 --- Lattice Structure --- p.28 / Chapter 3.1.3 --- Algorithm on Lattice Construction --- p.31 / Chapter 3.2 --- Pattern Matching --- p.32 / Chapter 3.2.1 --- Formulating the Problem of Similarity --- p.35 / Chapter 3.2.2 --- Error Measurement --- p.38 / Chapter 3.3 --- Indexing Scheme --- p.39 / Chapter 3.3.1 --- Indexing with scaling and shifting proposed by Chu and Wong --- p.40 / Chapter 3.3.2 --- Integrating with lattice structure --- p.41 / Chapter 3.4 --- Results --- p.43 / Chapter 4 --- Chart Patterns Searching for Chart Analysis --- p.47 / Chapter 4.1 --- Chart Patterns Overview --- p.47 / Chapter 4.1.1 --- Reversal Patterns --- p.49 / Chapter 4.1.2 --- Continuation Patterns --- p.52 / Chapter 4.2 --- Representation --- p.53 / Chapter 4.2.1 --- Trendline Preparation --- p.54 / Chapter 4.2.2 --- Trendline Pair --- p.59 / Chapter 4.3 --- Three-Phase Pattern Classification --- p.66 / Chapter 4.3.1 --- Phase One: Trendline Pair Classification --- p.66 / Chapter 4.3.2 --- Phase Two: Patterns Merging and Rejection --- p.74 / Chapter 4.3.3 --- Phase Three: Patterns Merging of Unclassified and Un- merged Trendline Pairs --- p.89 / Chapter 4.4 --- Results --- p.90 / Chapter 5 --- Conclusion --- p.100 / Chapter A --- Supplementary Results --- p.103 / Chapter A.1 --- Ascending Triangle --- p.103 / Chapter A.2 --- Descending Triangle --- p.104 / Chapter A.3 --- Falling Wedge --- p.106 / Chapter A.4 --- Head and Shoulders --- p.107 / Chapter A.5 --- Price Channel --- p.109 / Chapter A.6 --- Rectangle --- p.110 / Chapter A.7 --- Rising Wedge --- p.112 / Chapter A.8 --- Symmetric Triangle --- p.113 / Chapter A.9 --- Double Bottom --- p.113 / Chapter A.10 --- Double Top --- p.116 / Chapter A.11 --- Triple Bottom --- p.118 / Chapter A.12 --- Triple Top --- p.120 / Bibliography --- p.122 / Publications --- p.128

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Ho, Sin Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 49-52). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Autoregressive moving average time series --- p.1 / Chapter 1.2 --- Integrated stationary time series --- p.3 / Chapter 1.3 --- Some existing methods of identifying d --- p.4 / Chapter 1.4 --- Introduction to Cressie's --- p.6 / Chapter 1.5 --- Outline of thesis --- p.6 / Chapter 2 --- Variogram and Polyvariogram --- p.7 / Chapter 2.1 --- Introduction to variogram --- p.7 / Chapter 2.2 --- Polyvariogram of order b --- p.8 / Chapter 3 --- Testing Procedure --- p.10 / Chapter 3.1 --- Testing for an integrated white noise series --- p.10 / Chapter 3.2 --- Testing for an integrated ARM A series --- p.11 / Chapter 3.3 --- Testing for an integrated linear process --- p.12 / Chapter 4 --- Simulation Results --- p.14 / Chapter 4.1 --- Choice of series length n and r --- p.14 / Chapter 4.2 --- Integrated ARMA series --- p.21 / Chapter 4.3 --- Integrated linear process --- p.39 / Chapter 4.4 --- Comparisons with some methods in literatures --- p.43 / Chapter 4.5 --- An illustrative example --- p.45 / Chapter 5 --- Concluding Remark --- p.48 / Bibliography --- p.49