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題名 股價變化之波動的若干流體動力訊號–跨天效應
Some hydrodynamic signatures in fluctuations of stock price changes–crossing day effect
作者 吳培煜
Wu, Pei-Yu
貢獻者 馬文忠
Ma, Wen-Jong
吳培煜
Wu, Pei-Yu
關鍵詞 股票
盤後交易
動力參數
跨天
網路
Stock
After trading
Network
Crossing-day
Hydrodynamic
日期 2018
上傳時間 3-七月-2018 17:31:37 (UTC+8)
摘要 本論文探討 2004 年至 2009 年台灣市場(TWII)的股票群體報酬在 不同時間尺度下，類比於多粒子系統的擴散常數 D、動力溫度 θ 及移 動率 μ 等動力參數，並與 1996 年至 2001 年的美國、台灣、上海股市 的數據進行比較，研究不同市場中的共同特性。我們密集計算個股報 酬的高頻序列，其中序列時間點的間隔固定，計算報酬所採用的時間 間隔時間 τ 則作為時間尺度變數。我們分析不同年份的台灣與美國市 場、其交易日之間的跨天效應，發現跨天影響的重要性。我們檢視時 間序列的交易數據，得到跨天的影響廣泛的存在於不同時間、市場的 股票之中，藉由區分報酬數據是否跨天的情況、計算機率密度函數分 佈的尺度參數的變化，從中確認這兩種市場中的共同統計性質，並發 現跨天會使機率密度函數分佈呈現「不對稱」的特徵。我們發現跨天 的效應會使數據中地使價格差持續為正(或持續為負)，在計算時間的 統計分布中，透過盤後的等效交易時間tafter 可以有效量化跨天的效 應。
除了時間上的分析，本論文引入網路的概念把股票間的相關係數當 作連結強度，分析股票網路在(時間序列長度)T 的維度空間中之結 構，得到了股票網路中各節點(股票)的「不均質」特性，並透過一 個網路模型的建構程序，對這「不均值」的特性進行定性上的研究。 我們又引入時間的因素，同時考慮時間與空間上的相關性，並從中又 發現跨天與跨天間有影響的訊號，此與盤後的等效交易時間tafter 的 分析相互應，定量上確認了股票網路在時間上由跨天造成的「不均勻」的特性。
By the analogy of a system of many particles, we study the diffusion constant D, kinetic temperature θ and mobility μ obtained from the log-returns over different time scales for a collections of stocks in Taiwan market, over 2004- 2009. The values of these hydrodynamic parameters are compared with their counterparts for stocks in Taiwan, US and Shanghai markets from 1996 to 2001, to reveal their common properties. The sequences of returns of individual stocks are intensively evaluated, keeping the interval in between the time spots of the sequences fixed and treating the time τ over which the returns are calculated as the variable for time scales. We checked the time sequences of trading data and found that crossing-day effect is present in all points in time and market.By distinguishing between returns of crossing-day and those of non-crossing-day, the analysis both of scaling properties in probability functions and of the enhanced statistics of persistent time for up-trend (or down-trend) events as an effect caused by crossing-day contributions, show same features shared by Taiwan and US markets. The crossing-day effect makes the probability functions asymmetric. Such an efffect can be quantified by finding the effective after-market trading time tafter. In interpreting the cross correlation coefficient as the strength of the bond in between two stocks, a networks of stocks with continuous values in the bonds among the sites is introduced, which, in combination with model construction, helps to capture qualitatively the main features of stock-stock heterogeneity. In the analysis to include the temporal correlation as well as the stock-stock cross correlations, the crossing-day effect displays concrete signatures, which furtherly support the results revealed in the analysis of persistent time of up-trend events.
參考文獻 [1] L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potters, Noise dressing of financial corre- lation. Phys. Rev. Lett. 83 (1999) 1467-1470.
[2] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley, Universal and nonuniversal properties of cross correlations in financial time series. Phys. Rev. Lett. 83 (1999) 1471-1474.
[3] J. D. Noh, Model for correlations in stock markets. Phys. Rev. E 61, 5981 (2000).
[4] W. J. Ma, C. K. Hu, R. E. Amritkar, Stochastic dynamical model for stock-stock correlations. Phys. Rev. E 70 (2004) 26101.
[5] R. Engle, Financial econometrics - A new discipline with new methods. J. Econo- metrics 100 (2001) 53-56.
[6] W. J. Ma, S. C. Wang, C. N. Chen, C. K. Hu, Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation. EPL 102 (2013) 66003.
[7] Yu Feng Huang, Random walk model and underlying structure. Master Thesis (National ChengChi University, 2013).
[8] Steven Radelet, Jeffrey Sachs, The onset of the East Asian financial crisis. NBER Working Paper No. 6680 (1998).
[9] John V Duca, Subprime Mortgage Crisis 2006-2010. Federal Reserve History (2014).
https://www.federalreservehistory.org/essays/subprime_mortgage_crisis
[10] Yuliya Demyanyk, Otto Van Hemert, Understanding the Subprime Mortgage Cri- sis.The Review of Financial Studies 24 (2011) 1848–1880.
[11]Parameswaran Gopikrishnan, Vasiliki Plerou, Luis A. Nunes Amaral, Martin Meyer, and H. Eugene Stanley, Scaling of the distribution of fluctuations of financial market indices. Phys. Rev. E 60 (1999).
[12] Shwu-Jane Shieh, Shlomo Havlin, H. Eugene Stanley, Statistical analysis of the overnight and daytime return. Phys. Rev. E 79 (2009) 056109.
[13] M. G. Kendall, The analysis of economic time-series Part 1. Prices. Journal of the Royal Statistical Society 96 (1953) 11-25.
[14] Louis Bachelier, Theorie de la speculation. Gauthier-Villars. Annales Scientifiques de l’École Normale Supérieure 3 (1900) 21–86 .
[15] Albert Einstein, On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat. Physik 17 (1905) 549-560.
[16] R. N. Mantegna, H. E. Stanley, Scaling behavior in the dynamics of an economic index. Nature 376 (1995) 46-49.
[17] M. E. J, Newman: Networks an Introduction (Oxford University Press, 2010).
[18] Zhichen Sun, Continuous Transportation Network Design Problem Based on Bilevel Programming Model. Procedia Engineering 137 (2016) 277–282.
[19] Martin Gairing, Tobias Harks, and Max Klimm, Complexity and Approximation of the Continuous Network Design Problem. SIAM J. Optim. 27 (2017) 1554–1582.
[20] Linghui Han, Huijun Sun, Chengjuan Zhu, Jianjun Wu, The Continuous Network
Design Problem under the Traffic Network with Guidance System. 8th Interna- tional Conference on Traffic and Transportation Studies Changsha. (2012). arXiv: 1307.4258.
[21] J. J. Chen, L.Tan, W. J. Ma and C. K. Hu (private communication 2015) .
[22] 王碩濱. 以經濟物理學觀點分析臺灣股市日內時間序列 Analysis of Intraday time series in Taiwan stock market:Econophysics approach. Master Thesis (National Dong Hwa University, 2006).
[23] Wang, Bo Yuan, Statistical and Dynamical Properties of Re-turns Using High Frequency 1-day Moving Averages For Collections of U.S Stocks Over 1996-1999. Master Thesis (National ChengChi University, 2013).
[24] Yi-Fu Shih, Scaling of Event-Occurrence in Stock Market. Master Thesis (National Chengchi University, 2017).
描述 碩士
國立政治大學
應用物理研究所
104755009
資料來源 http://thesis.lib.nccu.edu.tw/record/#G1047550092
資料類型 thesis
dc.contributor.advisor 馬文忠zh_TW
dc.contributor.advisor Ma, Wen-Jongen_US
dc.contributor.author (作者) 吳培煜zh_TW
dc.contributor.author (作者) Wu, Pei-Yuen_US
dc.creator (作者) 吳培煜zh_TW
dc.creator (作者) Wu, Pei-Yuen_US
dc.date (日期) 2018en_US
dc.date.accessioned 3-七月-2018 17:31:37 (UTC+8)-
dc.date.available 3-七月-2018 17:31:37 (UTC+8)-
dc.date.issued (上傳時間) 3-七月-2018 17:31:37 (UTC+8)-
dc.identifier (其他 識別碼) G1047550092en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/118273-
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) 104755009zh_TW
dc.description.abstract (摘要) 本論文探討 2004 年至 2009 年台灣市場(TWII)的股票群體報酬在 不同時間尺度下，類比於多粒子系統的擴散常數 D、動力溫度 θ 及移 動率 μ 等動力參數，並與 1996 年至 2001 年的美國、台灣、上海股市 的數據進行比較，研究不同市場中的共同特性。我們密集計算個股報 酬的高頻序列，其中序列時間點的間隔固定，計算報酬所採用的時間 間隔時間 τ 則作為時間尺度變數。我們分析不同年份的台灣與美國市 場、其交易日之間的跨天效應，發現跨天影響的重要性。我們檢視時 間序列的交易數據，得到跨天的影響廣泛的存在於不同時間、市場的 股票之中，藉由區分報酬數據是否跨天的情況、計算機率密度函數分 佈的尺度參數的變化，從中確認這兩種市場中的共同統計性質，並發 現跨天會使機率密度函數分佈呈現「不對稱」的特徵。我們發現跨天 的效應會使數據中地使價格差持續為正(或持續為負)，在計算時間的 統計分布中，透過盤後的等效交易時間tafter 可以有效量化跨天的效 應。
除了時間上的分析，本論文引入網路的概念把股票間的相關係數當 作連結強度，分析股票網路在(時間序列長度)T 的維度空間中之結 構，得到了股票網路中各節點(股票)的「不均質」特性，並透過一 個網路模型的建構程序，對這「不均值」的特性進行定性上的研究。 我們又引入時間的因素，同時考慮時間與空間上的相關性，並從中又 發現跨天與跨天間有影響的訊號，此與盤後的等效交易時間tafter 的 分析相互應，定量上確認了股票網路在時間上由跨天造成的「不均勻」的特性。		zh_TW
dc.description.abstract (摘要) By the analogy of a system of many particles, we study the diffusion constant D, kinetic temperature θ and mobility μ obtained from the log-returns over different time scales for a collections of stocks in Taiwan market, over 2004- 2009. The values of these hydrodynamic parameters are compared with their counterparts for stocks in Taiwan, US and Shanghai markets from 1996 to 2001, to reveal their common properties. The sequences of returns of individual stocks are intensively evaluated, keeping the interval in between the time spots of the sequences fixed and treating the time τ over which the returns are calculated as the variable for time scales. We checked the time sequences of trading data and found that crossing-day effect is present in all points in time and market.By distinguishing between returns of crossing-day and those of non-crossing-day, the analysis both of scaling properties in probability functions and of the enhanced statistics of persistent time for up-trend (or down-trend) events as an effect caused by crossing-day contributions, show same features shared by Taiwan and US markets. The crossing-day effect makes the probability functions asymmetric. Such an efffect can be quantified by finding the effective after-market trading time tafter. In interpreting the cross correlation coefficient as the strength of the bond in between two stocks, a networks of stocks with continuous values in the bonds among the sites is introduced, which, in combination with model construction, helps to capture qualitatively the main features of stock-stock heterogeneity. In the analysis to include the temporal correlation as well as the stock-stock cross correlations, the crossing-day effect displays concrete signatures, which furtherly support the results revealed in the analysis of persistent time of up-trend events.en_US
dc.description.tableofcontents 中文摘要 1
Abstract ........ 3
Contents ........5
List of Figures ........ 7
2.1 1101 (台泥) 在 2018.4.30 的五分鐘交易線。資料來源:https:// tw.stock.yahoo.com/q/ta?s=1101.......... 7
2.2 The correlation of 386 stock for TWII for 2004y.(a)Raw data, (b)random model........25
3.1 The 386 stocks in TW for each month in 2004y-2009y. Scaled mean square log-returnvs.scaled time internal τ........ 30
3.2 The 386 stocks in TW for each month in 2004y-2009y. (b)Scaled mean square log-return vs. scaled time internal τ∗......... 31
3.3 Compare the fitted kinetic parameters, θ , D and μ of Taiwan, US and Shanghai stocks over a different period (1996y-1999y) and this work Taiwan(2004y-2009y)............. 32
3.4 Scaled Raw data PDF f ′ (r′ ) and scaled log-return r′ in TWII between 2004y-2007y......... 35
3.5 Scaled Raw data PDF f ′ (r′ ) and scaled log-return r′ in TWII between 2008y-2009y. .......... 36
3.6 Scaled CD PDF f ′ (r′ ) and scaled log-return r′ in TWII between 2004y- 2007y............ 36
3.7 Scaled CD PDF f ′ (r′ ) and scaled log-return r′ in TWII between 2008y- 2009y.......... 37
3.8 Scaled NOCD PDF f ′ (r′ ) and scaled log-return r′ in TWII between 2004y- 2007y.......... 37
3.9 Scaled NOCD PDF f ′ (r′ ) and scaled log-return r′ in TWII between 2008y- 2009y........... 38
3.10 Scaled raw data PDF f ′ (r′ ) and scaled log-return r′ in SP500 between 1996y-1999y. ........ 38
3.11 Scaled CD PDF f′(r′)and scaled log-return r′ in SP500 between 1996y- 1999y............ 39
3.12 Scaled NOCD PDF f′(r′) and scaled log-return r′ in SP500 between 1996y-1999y. ........... 39
4.1 Red line is Persistent time. Blue line is hitting time........... 45
4.2 Comparison two market TWII , SP500 with PDF vs Persistent time and log-PDF vs log-Persistent time............46
4.3 Log return r CD of crossing day schematic......... 47
4.4 PDF of Persistent time with data of real stocks and of fitted after-hours trading model in linear plots (upper panel) and log-log plots (lower panel) for TW market (left panel) and US market(right panel........... 48
4.5 PDF vs effective time in after-hours trading model........... 49
4.6 The correlation of 386 stock for TWII for 2004y.(a)Raw data, (b)random model...........52
4.7 The (a)correlation, (b)DV, (c)distance, (d)closeness centrality of 386 stock for TWII for 2004y-2009y...........53
4.8 The correlation of log-reutrn with τ = 100 calculation RCTC, SCTC,
RATC, SATC for TWII for 2004y-2009y...........59
4.9 RCTC and ACTC at different moment for TWII for 2004y-2009y ........... 60
5.1 The correlation with different τ of time sequence for TWII for 2004y-2009y...........64
A.1 PDF f (r) and log-return r for TWII for 2004y-2005y and get m of α from blue line...........70
A.2 PDF f (r) and log-return r for TWII for 2006y-2007y and get m of α from blue line...........71
A.3 PDF f (r) and log-return r for TWII for 2008y-2009y and get m of α from blue line...........71
A.4 PDF f(r) and log-return r of CD for TWII for 2004y-2005y ........... 72
A.5 PDF f(r) and log-return r of CD for TWII for 2006y-2007y ...........72
A.6 PDF f(r) and log-return r of CD for TWII for 2008y-2009y ........... 73
A.7 PDF f(r) and log-return r of NOCD for TWII for 2004y-2005y and get m of α from blue line........... 73
A.8 PDF f(r) and log-return r of NOCD for TWII for 2006y-2007y and get m of α from blue line...........74
A.9 PDF f(r) and log-return r of NOCD for TWII for 2008y-2009y and get m of α from blue line........... 74
A.10 PDF f(r) and log-return r for SP500 for Raw data 1996y-1997y........... 75
A.11 PDF f(r) and log-return r for SP500 for Raw data 1996y-1997y ........... 75
A.12PDFf(r)and log-return r for SP500 for CD 1996y-1997y ........... 76
A.13 PDF f(r) and log-return r for SP500 for CD 1998y-1999y ........... 76
A.14 PDF f(r) and log-return r for SP500 for NOCD 1996y-1997y ........... 77
A.15 PDF f(r) and log-return r for SP500 for NOCD 1998y-1999y ...........77
A.16 Comparison raw data, CD, NOCD for TWII for 2006y-2009y ........... 78
A.17 Comparison raw data, CD, NOCD for SP500 for 2006y-2009y ...........79
List of Tables 11
1 介紹 1
2 數據特性，理論背景及分析方法 5
2.1 資料來源................................ 5
2.1.1 資料採樣方法........................... 6
2.1.2 資料特性.............................. 7
2.1.3 跨天事件的分析方法 ..................... 8
2.2 隨機行走與布朗運動 ....................... 9
2.2.1 一維隨機行走.......................... 10
2.2.2 Langevin方程描述布朗運動 .............. 11
2.3 耦合隨機行走模型(Coupledrandomwalkmodel) .... 14
2.4 萊維穩定分佈(Lévystabledistribution)........ 15
2.5 網路分析方法 ............................... 17
2.5.1 網路中的連結度與鄰接矩陣 ................... 17
2.5.2 網路中心性 ............................ 18
2.5.3 連續性網路的建構過程..................... 23
2.6 盤後交易模型 ............................. 26
3 一整群股票的報酬之時間尺度性質 ...........29
3.1 由均方報酬的尺度變換計算動力參數........ 29
3.2 報酬的機率密度函數的尺度不變性 ......... 33
4 一整群股票的價格變動分析時間的不均勻與空間的不均質.... 44
4.1 上升趨勢事件的持續性時間 ..................... 44
4.2 以網路慨念分析股票間的交互相關性............... 50
4.3 股票交互的時間相關性......................... 57
5 結論與討論 ...........62
A 附錄 ...........70		zh_TW
dc.format.extent 6271718 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1047550092en_US
dc.subject (關鍵詞) 股票zh_TW
dc.subject (關鍵詞) 盤後交易zh_TW
dc.subject (關鍵詞) 動力參數zh_TW
dc.subject (關鍵詞) 跨天zh_TW
dc.subject (關鍵詞) 網路zh_TW
dc.subject (關鍵詞) Stocken_US
dc.subject (關鍵詞) After tradingen_US
dc.subject (關鍵詞) Networken_US
dc.subject (關鍵詞) Crossing-dayen_US
dc.subject (關鍵詞) Hydrodynamicen_US
dc.title (題名) 股價變化之波動的若干流體動力訊號–跨天效應zh_TW
dc.title (題名) Some hydrodynamic signatures in fluctuations of stock price changes–crossing day effecten_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potters, Noise dressing of financial corre- lation. Phys. Rev. Lett. 83 (1999) 1467-1470.
[2] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley, Universal and nonuniversal properties of cross correlations in financial time series. Phys. Rev. Lett. 83 (1999) 1471-1474.
[3] J. D. Noh, Model for correlations in stock markets. Phys. Rev. E 61, 5981 (2000).
[4] W. J. Ma, C. K. Hu, R. E. Amritkar, Stochastic dynamical model for stock-stock correlations. Phys. Rev. E 70 (2004) 26101.
[5] R. Engle, Financial econometrics - A new discipline with new methods. J. Econo- metrics 100 (2001) 53-56.
[6] W. J. Ma, S. C. Wang, C. N. Chen, C. K. Hu, Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation. EPL 102 (2013) 66003.
[7] Yu Feng Huang, Random walk model and underlying structure. Master Thesis (National ChengChi University, 2013).
[8] Steven Radelet, Jeffrey Sachs, The onset of the East Asian financial crisis. NBER Working Paper No. 6680 (1998).
[9] John V Duca, Subprime Mortgage Crisis 2006-2010. Federal Reserve History (2014).
https://www.federalreservehistory.org/essays/subprime_mortgage_crisis
[10] Yuliya Demyanyk, Otto Van Hemert, Understanding the Subprime Mortgage Cri- sis.The Review of Financial Studies 24 (2011) 1848–1880.
[11]Parameswaran Gopikrishnan, Vasiliki Plerou, Luis A. Nunes Amaral, Martin Meyer, and H. Eugene Stanley, Scaling of the distribution of fluctuations of financial market indices. Phys. Rev. E 60 (1999).
[12] Shwu-Jane Shieh, Shlomo Havlin, H. Eugene Stanley, Statistical analysis of the overnight and daytime return. Phys. Rev. E 79 (2009) 056109.
[13] M. G. Kendall, The analysis of economic time-series Part 1. Prices. Journal of the Royal Statistical Society 96 (1953) 11-25.
[14] Louis Bachelier, Theorie de la speculation. Gauthier-Villars. Annales Scientifiques de l’École Normale Supérieure 3 (1900) 21–86 .
[15] Albert Einstein, On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat. Physik 17 (1905) 549-560.
[16] R. N. Mantegna, H. E. Stanley, Scaling behavior in the dynamics of an economic index. Nature 376 (1995) 46-49.
[17] M. E. J, Newman: Networks an Introduction (Oxford University Press, 2010).
[18] Zhichen Sun, Continuous Transportation Network Design Problem Based on Bilevel Programming Model. Procedia Engineering 137 (2016) 277–282.
[19] Martin Gairing, Tobias Harks, and Max Klimm, Complexity and Approximation of the Continuous Network Design Problem. SIAM J. Optim. 27 (2017) 1554–1582.
[20] Linghui Han, Huijun Sun, Chengjuan Zhu, Jianjun Wu, The Continuous Network
Design Problem under the Traffic Network with Guidance System. 8th Interna- tional Conference on Traffic and Transportation Studies Changsha. (2012). arXiv: 1307.4258.
[21] J. J. Chen, L.Tan, W. J. Ma and C. K. Hu (private communication 2015) .
[22] 王碩濱. 以經濟物理學觀點分析臺灣股市日內時間序列 Analysis of Intraday time series in Taiwan stock market:Econophysics approach. Master Thesis (National Dong Hwa University, 2006).
[23] Wang, Bo Yuan, Statistical and Dynamical Properties of Re-turns Using High Frequency 1-day Moving Averages For Collections of U.S Stocks Over 1996-1999. Master Thesis (National ChengChi University, 2013).
[24] Yi-Fu Shih, Scaling of Event-Occurrence in Stock Market. Master Thesis (National Chengchi University, 2017).		zh_TW
dc.identifier.doi (DOI) 10.6814/THE.NCCU.AP.001.2018.B04-