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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張嘉升(Chia-Seng Chang) | |
| dc.contributor.author | Chih-Hao Lin | en |
| dc.contributor.author | 林志豪 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:22:23Z | - |
| dc.date.available | 2014-03-09 | |
| dc.date.copyright | 2014-03-09 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-01-27 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58617 | - |
| dc.description.abstract | 本篇論文主要是在研究複雜系統的隨機度分析及應用。首先我們會從機率理論、布朗運動和隨機過程出發，去探討一些基本的時間序列特性。接著我們會用提出方法去探討非穩態時間序列的特性。所謂的非穩態的時間序列是指其平均值和標準差是時間的函數，而不是常數。除此之外，我們也利用開發出的方法去分析不同種的時間序列，例如股票市場和心律變動性分析。利用一些股票市場的特性，我們提出了一種適合保守型投資者的投資策略，此策略可以避免投資者承受金融海嘯的損失並且其交易結果優於大多數的股票平均。在心律變動分析方面，我們所提出的方法可以精準地分辨出睡眠呼吸中止症的患者和一般民眾的心跳節奏的不同，因此可以在醫學上有很大的應用潛力。在本篇論文的最後，我們附上一些我們使用過的數值方法和程式碼，以方便讀者可以輕鬆地重複我們的一些研究成果。 | zh_TW |
| dc.description.abstract | The main theme of this thesis is about the study of stochasticity in complex systems and its applications. First, we introduce the probability theory, Brownian motions, Ito process and multifractal random walk model, which are the basic models to describe the stochastic behavior of the time series. Then we develop methods to study the properties of the non-stationary time series, of which the mean and variance are changing with time, and quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. In addition, we make use of the properties we found in the time series of stock market to propose a trading strategy to avoid losing fortune in the bear market and the overall trading results beat the average performance of the stock markets. We apply our algorithms to study the heart rate variability(HRV) in cardiology system. Our results can be used to distinguish the difference between the HRV of the healthy people and the patients with sleep apnea symptom. We introduce some numerical methods in the appendices we used in studying the time series such as optimization methods and clustering phenomena. This thesis is organized as follows. In Chapter 1, we introduce the stochastic process and the multifractal random walk. In Chapter 2, we introduce our algorithms to measure the stochasticity in the non-stationary time series and its properties. In Chapter 3 and Chapter 4, we present the applications of our algorithms. A trading strategy which can be applied to any stock markets is introduced in Chapter 3. We define a parameter to distinguish the difference between the HRV of the healthy people and the patients with sleep apnea symptom in Chapter 4. Chapter 5 is the conclusion of our works in this thesis. In Chapter 6 (Appendix 1), we introduce a numerical method to solve optimization problems: the Genetic algorithm. In Chapter 7 (Appendix 2), we introduce the clustering effect which is the cause of the long term correlations and its applications. Chapter 8 (Appendix 3) is some miscellaneous contents which contain several useful functions and the Matlab source codes employed in the analysis and simulation in this thesis. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:22:23Z (GMT). No. of bitstreams: 1 ntu-103-D99222013-1.pdf: 1871156 bytes, checksum: 89010524d8158a3042ab88367fcd2323 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 序言及致謝 i
中文摘要 ii ABSTRACT iii CONTENTS v LIST OF FIGURES viii LIST OF TABLES x Chapter 1 Stochastic process 1 1.1 Introduction 1 1.2 Multifractal random walk (MRW) 9 Chapter 2 Algorithms to study stochasticity and multifractality in complex systems 19 2.1 Introduction 19 2.2 Method 24 2.3 Simulated time series test 29 2.4 Results 31 2.5 Conclusion 42 Chapter 3 Application: Adaptive trading for anti-correlated pairs of stocks 45 3.1 Introduction 45 3.2 First criterion on investment 47 3.3 Stock-pair selection: variance analysis for the long time scale 49 3.4 Short term trading criterion 51 3.5 Simulation result 53 3.6 Conclusion 58 Chapter 4 Application: The heart rate variability analysis of sleep apnea patients 59 4.1 Introduction 59 4.2 Methodology 60 4.3 Results and conclusion 62 Chapter 5 Conclusion 70 Chapter 6 Appendix (1) : Genetic algorithms 73 6.1 Introduction 73 6.2 Genetic algorithms 75 6.3 An example: Berg’s equation 78 6.4 Conclusion 81 Source code (Matlab) 82 Chapter 7 Appendix (2): Clustering effect and its applications 84 7.1 Introduction 84 7.2 Clustering behavior and autocorrelation function 88 7.3 Quantitative measurement of clustering behavior 92 7.4 The application of clustering index 97 Chapter 8 Appendix (3) Miscellany 102 8.1 Correlation function 102 8.2 Clustering index 104 8.3 Distribution function 106 8.4 Import and export data file 107 8.5 Moving window method 108 8.6 Kolmogorov-Smirnov test 109 8.7 Fluctuation analysis and Hurst exponent 110 8.8 Generating correlated random number 111 References 113 | |
| dc.language.iso | en | |
| dc.title | 量測複雜系統隨機度與多重碎形維度之演算法開發與應用 | zh_TW |
| dc.title | An Empirical Algorithm to Measure Stochasticity and Multifractality in Complex Systems and Its Applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.coadvisor | 李世炳(Sai-Ping Li) | |
| dc.contributor.oralexamcommittee | 龐寧寧(Ning-Ning Pang),林致廷(Chih-Ting Lin),王孫崇(Sun-Chong Wang) | |
| dc.subject.keyword | 隨機過程,時間序列,隨機度,交易策略,心律變動性分析, | zh_TW |
| dc.subject.keyword | stochastic process,non-stantionary time series,Wiener process,conservative trading strategy,heart rate variability,sleep apnea, | en |
| dc.relation.page | 122 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-01-27 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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