使用區間型時間序列資料偵測改變點

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：103

、訪客IP：3.129.42.198

姓名

黃宗元(Zong-Yuan Huang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

使用區間型時間序列資料偵測改變點
(Change Point Detection with Financial Interval Time Series)

相關論文

★ Credit Risk Illustrated under Coupled diffusions	★ The analysis of log returns using copula-based Markov models
★ Systemic risk with relative behavior	★ 在厚尾分配下的均值收斂交易策略
★ Comparison of Credit Risk in Coupled Diffusion Model and Merton′s Model	★ Estimation in copula-based Markov mixture normal model
★ 金融系統性風險的回顧分析	★ New insights on ′′A semi-parametric model for wearable sensor-based physical activity monitoring data with informative device wear"
★ A parametric model for wearable sensor-based physical activity monitoring data with informative device wear	★ Optimal Asset Allocation using Black-Litterman with Smooth Transition Model
★ VIX Index Analysis using Copula-Based Markov Chain Models	★ 使用雙重指數平滑預測模型及無母數容忍限的配對交易策略
★ Intraday Pairs Trading on Taiwan Semiconductor Companies through Mean Reverting Processes	★ Target index tracing through portfolio optimization
★ Estimation in Copula-Based Markov Models under Weibull Distributions	★ Optimal Strategies for Index Tracking with Risky Constrains

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

在財務時間序列中，如果某些事件導致數據從一種特定分佈轉變為另一種分
佈，則該點稱為變化點。為了估計變化點，我們提出了一種區間型時間序列模型，該模型由每日的最高價、最低價和收盤價組成。基於假設日內對數價格由幾何布朗運動，並使用Girsanov 定理，我們推導了相應的似然函數。最大似然估計（MLEs）使用牛頓-拉弗森法方法獲得。在模擬研究中，我們觀察到所提出的方法在平均方根誤差（RMSE）方面優於僅使用收盤價和開盤價的方法。最後，在實際數據分析中，我們檢測了不同時期標普500 指數跟比特幣的變化點，包括2008 年金融危機、2020 年COVID-19 大流行和2022 年俄烏戰爭，以作為說明。

摘要(英)

To identify the change-point for the structure change in financial time series. We propose a symbolic time series model, where the model consists of the daily maximum, minimum, and closing prices. The corresponding likelihood function is derived based on the assumption that the intraday price is driven by geometric Brownian motion. The
likelihood function is obtained by using the Girsanov theorem. The maximum likelihood estimates are solved by the Newton-Raphson method. In simulation studies, we observe that the proposed method outperforms the method based on only the closing and opening prices in terms of smaller RMSE. Finally, in real data analysis, we detect change-points for the S&P 500 index and Bitcoin in varied time periods, including the 2008 financial crisis, the 2020 COVID-19 pandemic, and the 2022 Russo-Ukrainian War, for illustration.

關鍵字(中)

★ 改變點
★ 牛頓-拉弗森法，
★ 區間型時間序列
★ 幾何布朗運動

關鍵字(英)

★ Change point,
★ Newton-Raphson method
★ interval time series
★ geometric Brownian motion

論文目次

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Proposal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Change Point Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Geometric Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Maximum Likelihood Estimator . . . . . . . . . . . . . . . . . . . . . . . 8
3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Empirical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 S&P 500 index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Bitcoin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Appendix A The first order derivative . . . . . . . . . . . . . . . . . . . . . . . 38
Appendix B The second order derivative . . . . . . . . . . . . . . . . . . . . . . 41
Appendix C First and second derivatives of transformed log likelihood function 48

參考文獻

Ait-Sahalia, Y., Mykland, P. A. & Zhang, L. (2005). How often to sample a continuous-time
process in the presence of market microstructure noise. The review of financial studies,
18(2), 351–416.
Andersen, T. G., Bollerslev, T., Diebold, F. X. & Ebens, H. (2001). The distribution of
realized stock return volatility. Journal of financial economics, 61(1), 43–76.
Berger, R. L. & Casella, G. (2001). Statistical inference. Duxbury.
Billingsley, P. (1961). Statistical methods in markov chains. The annals of mathematical
statistics, 12–40.
Chen, C. W., Gerlach, R. & Lin, E. M. (2008). Volatility forecasting using threshold heteroskedastic
models of the intra-day range. Computational Statistics & Data Analysis,
52(6), 2990–3010.
Cheung, Y.-W. (2007). An empirical model of daily highs and lows. International Journal
of Finance & Economics, 12(1), 1–20.
Chou, R. Y. (2005). Forecasting financial volatilities with extreme values: the conditional
autoregressive range (carr) model. Journal of Money, Credit and Banking, 561–582.
Chou, R. Y. (2006). Modeling the asymmetry of stock movements using price ranges. In
Econometric analysis of financial and economic time series (pp. 231–257). Emerald
Group Publishing Limited.
Chou, R. Y. & Liu, N. (2010). The economic value of volatility timing using a range-based
volatility model. Journal of Economic Dynamics and Control, 34(11), 2288–2301.
Emura, T., Lai, C.-C. & Sun, L.-H. (2023). Change point estimation under a copula-based
markov chain model for binomial time series. Econometrics and Statistics, 28, 120–
137.
Garman, M. B. & Klass, M. J. (1980). On the estimation of security price volatilities from
historical data. Journal of business, 67–78.
Gilbert, J. C. & Lemaréchal, C. (1989). Some numerical experiments with variable-storage
quasi-newton algorithms. Mathematical programming, 45(1), 407–435.
Helfrick, A. D. & Cooper, W. D. (1996). Modern electronic instrumentation and measurement
techniques prentice-hall of india pvt. Ltd., New Delhi.
Itô, K. (1944). 109. stochastic integral. Proceedings of the Imperial Academy, 20(8), 519–
524.
Karatzas, I. & Shreve, S. (2014). Brownian motion and stochastic calculus (Vol. 113).
springer.
Lin, L.-C. & Sun, L.-H. (2019). Modeling financial interval time series. Plos one, 14(2),
e0211709.
Maruddani, D. & Trimono. (2018). Modeling stock prices in a portfolio using multidimensional
geometric brownian motion. In Journal of physics: Conference series (Vol.
1025, p. 012122).
Nagaraj, N. (1990). Two-sided tests for change in level for correlated data. Statistical Papers,
31, 181–194.
Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100–115.
Peng, C. & Simon, C. (2024). Financial modeling with geometric brownian motion. Open
Journal of Business and Management, 12(2), 1240–1250.
Perreault, L., Bernier, J., Bobée, B. & Parent, E. (2000). Bayesian change-point analysis
in hydrometeorological time series. part 1. the normal model revisited. Journal of Hydrology, 235(3-4), 221–241.
Perry, M. B. & Pignatiello Jr, J. J. (2005). Estimation of the change point of the process fraction
nonconforming in spc applications. International Journal of Reliability, Quality
and Safety Engineering, 12(02), 95–110.
Pignatiello Jr, J. J. & Samuel, T. R. (2001). Identifying the time of a step-change in the
process fraction nonconforming. Quality Engineering, 13(3), 357–365.
Reddy, K. & Clinton, V. (2016). Simulating stock prices using geometric brownian motion:
Evidence from australian companies. Australasian Accounting, Business and Finance
Journal, 10(3), 23–47.
Santner, T. J., Williams, B. J., Notz, W. I. & Williams, B. J. (2003). The design and analysis
of computer experiments (Vol. 1). Springer.
Shao, X. & Zhang, X. (2010). Testing for change points in time series. Journal of the
American Statistical Association, 105(491), 1228–1240.
Soltanifar, M. & Knight, K. (n.d.). A collection of exercises in advanced mathematical
statistics: The solution manual of all odd-numbered exercises from” mathematical
statistics”(2000). Chapman & Hall/CRC Press LLC.

指導教授

孫立憲(Li-Hsien Sun)

審核日期

2024-7-25

推文