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| Title: | 記憶效應下馬可夫鏈的尺度不變性初探
A Study of Scaling Behavior in Binary Markov Chains caused by Memory Effect |
| Authors: | 馮信堯
Feng, Hsin-Yao |
| Contributors: | 馬文忠
Ma, Wen-Jong
馮信堯
Feng, Hsin-Yao |
| Keywords: | 二位元序列
滾動視窗
埃倫費斯特模型
馬可夫鏈
縮放行為
Binary sequence
Rolling window
Ehrenfest urn model
Markov chain
Scaling behavior |
| Date: | 2023 |
| Issue Date: | 2023-09-01 16:27:34 (UTC+8) |
| Abstract: | 透過滾動視窗逐步生成的方式，我們產生一組"0"與"1"的二位元序列，其每一步新位元由前幾步的位元以機率性的方式決定，最終序列會收斂至特定狀態，此過程可以透過廣義的埃倫費斯特模型的物理機制來理解。此機制決定新的位元係由由"0"與"1"個數的比例決定，其中較少的具有較高的機率出現（既少數決定規則），此程序會趨向一種穩定狀態，即"0"與"1"出現的機會相等的狀態，此過程為一種負回饋機制，相當於是一種擴散過程。若將此機制改成正回饋機制（既多數決定規則），此序列將收斂至其中一個全為"0"或全為"1"的狀態。這種過程中的自我放大的機制能夠捕捉金融市場不穩定性的主要特徵。我們特別考慮到的是，兩種反饋機制控制的收斂過程均顯示出尺度不變性的特性。
A series of binary digits generated sequentially with its next bit determined probabilistically by the preceding bits within a rolling window, will converge to specific sets of states, that can be comprehended by the physics of Urn models. A sequence with its new bit determined by a probabilistic minority rule converges to the states with equal probability, to have either of the two binary digits ("0" and "1"). Such a process, with its new bit produced by a procedure of negative feedback, is equivalent to that of diffusion. The process to produce a sequence via a probabilistic majority rule (a procedure of positive feedback), on the other hand, leads the sequence to converge to the states, with probability exact one, to have exclusive only one of the two binary digits. The self-amplified effect in the process captures the major feature in an unstable situation in financal markets. The convergences, governed by either of the two kinds of feedback procedures, are found to show scaling behavior. |
| Reference: | [Bachelier, 1900] Bachelier, L. (1900). Theorie de la sp ´ eculation. In ´ Annales scientifiques
de l’Ecole normale sup ´ erieure ´ , volume 17, pages 21–86.
[Black and Scholes, 1973] Black, F. and Scholes, M. (1973). The pricing of options and
corporate liabilities. Journal of political economy, 81(3):637–654.
[Chen, 2015] Chen, C.-W. (2015). Time characteristic in cross correlation of stock fluctuations. Master’s thesis, National Chengchi University.
[Hod and Keshet, 2004] Hod, S. and Keshet, U. (2004). Phase transition in random walks
with long-range correlations. Physical Review E, 70(1):015104.
[Kac, 1947] Kac, M. (1947). Random walk and the theory of brownian motion. The
American Mathematical Monthly, 54(7P1):369–391.
[Keshet and Hod, 2005] Keshet, U. and Hod, S. (2005). Survival probabilities of historydependent random walks. Physical Review E, 72(4):046144.
[Laloux et al., 1999] Laloux, L., Cizeau, P., Bouchaud, J.-P., and Potters, M. (1999).
Noise dressing of financial correlation matrices. Physical review letters, 83(7):1467.
[Lay et al., 2016] Lay, D. C., Lay, S. R., and McDonald, J. J. (2016). Linear algebra and
its applications. Pearson.
[Li, 2021] Li, Y.-C. (2021). A primitive study of memory effect of run of ones in binary
sequences. Master’s thesis, National Chengchi University
[Lutz and Ciliberto, 2015] Lutz, E. and Ciliberto, S. (2015). Information: From
maxwell’s demon to landauer’s eraser. Physics Today, 68(9):30–35.
[Ma et al., 2004] Ma, W.-J., Hu, C.-K., and Amritkar, R. E. (2004). Stochastic dynamical
model for stock-stock correlations. Physical Review E, 70(2):026101.
[Ma et al., 2013] Ma, W.-J., Wang, S.-C., Chen, C.-N., and Hu, C.-K. (2013). Crossover
behavior of stock returns and mean square displacements of particles governed by the
langevin equation. Europhysics Letters, 102(6):66003.
[Mandelbrot, 1960] Mandelbrot, B. (1960). The pareto-levy law and the distribution of
income. International economic review, 1(2):79–106.
[Mandelbrot, 1963] Mandelbrot, B. (1963). New methods in statistical economics. Journal of political economy, 71(5):421–440.
[Mandelbrot, 2013] Mandelbrot, B. B. (2013). Fractals and scaling in finance: Discontinuity, concentration, risk. Selecta volume E. Springer Science & Business Media.
[Mantegna and Stanley, 1995] Mantegna, R. N. and Stanley, H. E. (1995). Scaling behaviour in the dynamics of an economic index. Nature, 376(6535):46–49.
[Osborne, 1967] Osborne, M. (1967). Some quantitative tests for stock price generating models and trading folklore. Journal of the American Statistical Association,
62(318):321–340.
[Osborne, 1959] Osborne, M. F. (1959). Brownian motion in the stock market. Operations
research, 7(2):145–173.
[Papoulis and Unnikrishna Pillai, 2002] Papoulis, A. and Unnikrishna Pillai, S. (2002).
Probability, random variables and stochastic processes.
[Plerou et al., 1999] Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., and
Stanley, H. E. (1999). Universal and nonuniversal properties of cross correlations in
financial time series. Physical review letters, 83(7):1471.
[Sagawa, 2012] Sagawa, T. (2012). Thermodynamics of information processing in small
systems. Progress of theoretical physics, 127(1):1–56.
[Shih, 2017] Shih, Y.-F. (2017). Scaling of event-occurrence in stock market. Master’s
thesis, Shih, Yi-Fu.
[Sornette, 2009] Sornette, D. (2009). Why stock markets crash: critical events in complex
financial systems. Princeton university press.
[Strang, 2006] Strang, G. (2006). Linear algebra and its applications. Belmont, CA:
Thomson, Brooks/Cole.
[West, 2018] West, G. (2018). Scale: The universal laws of life, growth, and death in
organisms, cities, and companies. Penguin.
[Wu, 2018] Wu, P.-Y. (2018). Some hydrodynamic signatures in fluctuations of stock
price changes–crossing day effect. Master’s thesis, National Chengchi University.
[Zivot et al., 2003] Zivot, E., Wang, J., Zivot, E., and Wang, J. (2003). Rolling analysis
of time series. Modeling financial time series with S-Plus®, pages 299–346.
[李政道, 2006] 李政道 (2006). 李政道講義：統計力學. 上海科學技術出版社.
[林清涼, 2014] 林清涼 (2014). 從物理學切入的線性代數導論. 五南圖書. |
| Description: | 碩士
國立政治大學
應用物理研究所
109755008 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109755008 |
| Data Type: | thesis |
| Appears in Collections: | [Graduate Institute of Applied Physics] Theses
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