| dc.contributor.advisor | 馬文忠 | zh_TW |
| dc.contributor.advisor | Ma,Wen-Jong | en_US |
| dc.contributor.author (Authors) | 李雨純 | zh_TW |
| dc.contributor.author (Authors) | Li,Yu-Chun | en_US |
| dc.creator (作者) | 李雨純 | zh_TW |
| dc.creator (作者) | Li, Yu-Chun | en_US |
| dc.date (日期) | 2021 | en_US |
| dc.date.accessioned | 2-Mar-2021 14:34:21 (UTC+8) | - |
| dc.date.available | 2-Mar-2021 14:34:21 (UTC+8) | - |
| dc.date.issued (上傳時間) | 2-Mar-2021 14:34:21 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0104755001 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/134091 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用物理研究所 | zh_TW |
| dc.description (描述) | 104755001 | zh_TW |
| dc.description.abstract (摘要) | 在複雜的金融系統中，許多變動因素影響著市場，人們在揭開這些因素的努力中觀察到許多典型化的實況(stylized facts)；其中一個重要的結果為:各種計量的分布呈現著冪次定律(power-law)。本論文回歸到一個基本的問題:在簡單的布朗運動中是否能夠、或者如何產生冪次定律的特性；藉由將股價的下跌與上漲視為二位元的0與1，將一支股票的時間演變，視為一個二位元序列，所要分析的就變成序列中連續1的分布性質。我們的模型中，在某一時間點的下一個位元(股價變動)，可以是任意產生(交易不依靠記憶)或是根據交易歷史來決定(根據記憶進行交易)；這樣的時間序列最終會收斂到某種穩定狀態。我們發現，有記憶的序列，其抵達收斂狀態的平均時間與記憶長度呈現冪次定律的關係，而在不同記憶長度下得到的抵達時間之機率密度函數，在經過尺度轉換後，其曲線彼此間有很好的重疊性。此結果顯示金融數據所呈現的冪次定律分布，或可連結到系統內在的尺度不變性。 | zh_TW |
| dc.description.abstract (摘要) | In a complex financial system, there are many changing factors that are responsible for the time evolution of the market. There have been efforts to reveal those factors, which result in the observations of many “stylized facts”. One important observation is the presence of power laws in the distributions of various quantities. In this thesis, the author chose to explore such properties on a fundamental level to find whether, or how power laws can be generated in simple Brownian motion. The author uses a one-dimensional model to explore the fall and rise of stock prices, treating them as 0 and 1 in binary, respectively. The time evolution of the price changes of a stock is then realized as a binary sequence. The analysis goes to find the distributions of runs of ones (sections of consecutive ones) in binary sequences. In our model, the next bit (price change) at each time step is determined, either at random (trading without memory) or in accord with the history (trading with memory). The time sequence eventually converges to some steady state. It is found in this study that, for the sequences with memory, the mean arrival time of convergence is a power law function of the memory length. After scale transformation, the curves of the probability density distributions of arrival times for different memory lengths overlap with each other nicely. The result suggests the power-law properties in the distributions of financial data may be related to some underlying scaling behavior of the system. | en_US |
| dc.description.tableofcontents | 第一章 緒論 1第二章 理論背景與原理 42.1與事件次數發生相關的分布 42.1.1伯努利試驗與二項分布(Binomial distribution)42.1.2卜瓦松分布(Poisson distribution)52.1.3幾何分佈(Geometric distribution)62.1.4負二項分布(negative binomial)72.2與時間有關的連續型分布72.2.1指數分佈(Exponential distribution)72.2.2布朗運動與一維隨機行走(Brownian Motion)82.2.3常態分佈(高斯分佈)(Normal distribution)92.2.4萊維穩定分布 (Lévy Stable Distribution)10第三章 二位元序列中的連續列探討113.1出現給定長度連續1所需的等待時間113.1.1第一次出現給定長度連續1所需的等待時間123.1.2第 次出現給定長度連續1所需的等待時間133.2樣本空間的分析與模擬143.2.1完整連續列的樣本空間153.2.2次連續列(subsequence)的樣本空間153.2.3電腦模擬:以單一的長序列產生樣本空間中短序列連續1(run of ones)的分布17第四章 二位元序列的隨機過程與記憶效應194.1固定記憶長度m的隨機過程，連續列的分布過程為指數函數204.2全記憶的模擬:立即更新與變動更新214.3有限記憶( m > 1 且固定)二位元序列的長時間收斂分析254.3.1有限記憶二位元序列的時間演進254.3.2固定記憶二位元序列的隨機過程分析：轉移矩陣(transition matrix)294.3.3固定記憶二位元序列的隨機過程分析:Tarrival31第五章 結論34附錄A35附錄B40附錄C44附錄D45附錄E46參考文獻48 | zh_TW |
| dc.format.extent | 2822685 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0104755001 | en_US |
| dc.subject (關鍵詞) | 二位元字串 | zh_TW |
| dc.subject (關鍵詞) | 連續列 | zh_TW |
| dc.subject (關鍵詞) | 持續時間 | zh_TW |
| dc.subject (關鍵詞) | 冪次定律 | zh_TW |
| dc.title (題名) | 二位元序列中連續1的記憶效應初探 | zh_TW |
| dc.title (題名) | A primitive study of memory effect of run of ones in binary sequences | en_US |
| dc.type (資料類型) | thesis | en_US |
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| dc.identifier.doi (DOI) | 10.6814/NCCU202100266 | en_US |
