基於 Copula 下的馬可夫鏈模型對於負二項序列數據之改變點偵測

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：34

、訪客IP：52.14.201.233

姓名

謝帛翰(Po-Han Hsieh) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

基於 Copula 下的馬可夫鏈模型對於負二項序列數據之改變點偵測
(Change Point Estimation Based on the Copula-based Markov Chain Model for Negative Binomial 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)

本研究介紹了一種新穎的方法，用於估計負二項時間序列數據中的改變點，採用 Copula 馬可夫鏈模型。負二項分佈在描述過度離散的計數數據方面非常有效。在本研究中，我們應用了牛頓法作為實施方法，並利用漸近正態性方法獲得區間估計。負二項時間序列具有重要的實際應用意義；然而，準確估計其改變點一直是一個具有挑戰性的問題。本研究旨在通過提出一種可行的方法來確定負二項時間序列數據中的改變點，以解決這一問題。通過本研究，我們希望為負二項時間序列中的改變點估計問題提供可靠的解決方案，並為相關領域的研究和實踐提供有價值的參考。模擬結果表明，所提出的方法在檢測變點方面表現出高度精確性，超越了傳統方法，具有顯著的優勢。最後，我們使用了2020年COVID-19大流行的死亡數據以及1851年至1962年期間英國煤礦事故中工人死亡的112年數據進行實證分析。

摘要(英)

This study introduces a novel approach for estimating change points for negative binomial time series data, with the Copula Markov Chain model. The negative binomial distribution is highly effective in describing over-dispersed count data. In this study, we apply Newton′s method to solve the Maximum likelihood estimation (MLE) and the asymptotic normality method to obtain interval estimates. Negative binomial time series have significant practical implications; however, accurate estimation of their change points is a challenging problem. This research seeks to address this deficiency by presenting a viable approach for determining change points. Through this research, we provide a reliable solution for the change point estimation problem in negative binomial time series and offer valuable references for research and practice in the related fields. The results in the simulation studies demonstrate that the method exhibits a high level of precision in detecting change points. Finally, we use death data during the COVID-19 pandemic in 2020 and data on worker deaths from British coal mine accident over a 112-year period from 1851 to 1962 in empirical analysis for illustration.

關鍵字(中)

★ 變點估計
★ 馬可夫鏈模型
★ Clayton Copula
★ 牛頓-拉夫森方法
★ 負二項分佈

關鍵字(英)

★ Change Point Estimation
★ Markov Chain Model
★ Clayton Copula
★ Newton-Raphon Method
★ Negative Binomial

論文目次

Contents
1 Introduction 1
2 Proposed Model 4
2.1 CopulaFunction ................................ 4
2.2 ProposedChangePointModel......................... 5
2.3 Newton-Raphson(NR)Method......................... 9
2.4 AsymptoticNormalApproximationInterval . . . . . . . . . . . . . . . . . 11
3 Simulation Study 14
3.1 Setting...................................... 14
3.2 SimulationResults ............................... 15
3.3 ModelMisspecification ............................. 21
4 Empirical Study 23
4.1 Britishcoalmineaccidentdata ........................ 23 4.2 Taiwan’sCOVID-19pandemic......................... 26
5 Conclusion 30
Appendix A 33
Appendix B 34

參考文獻

Billingsley, P. (1961). On the coding theorem for the noiseless channel. The Annals of Mathematical Statistics, 32(2), 594–601.
Carlin, B. P., Gelfand, A. E., & Smith, A. F. (1992). Hierarchical bayesian analysis of changepoint problems. Journal of the Royal Statistical Society: Series C (Applied Statistics), 41(2), 389–405.
Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65(1), 141–151.
Darsow, W. F., Nguyen, B., & Olsen, E. T. (1992). Copulas and markov processes. Illinois Journal of Mathematics, 36(4), 600–642.
Hilbe, J. M. (2011). Negative Binomial Regression. Cambridge University Press.
Huang, X.-W., & Emura, T. (2021). Model diagnostic procedures for copula-based markov chain models for statistical process control. Communications in Statistics-Simulation and Computation, 50(8), 2345–2367.
Lavielle, M., & Teyssiere, G. (2007). Adaptive detection of multiple change-points in asset price volatility. In Long memory in economics (pp. 129–156). Springer.
Lee, S., Park, S., & Chen, C. W. (2017). On fisher’s dispersion test for integer-valued autoregressive poisson models with applications. Communications in Statistics-Theory and Methods, 46(20), 9985–9994.
MacDonald, I. L. (2014). Does newton–raphson really fail? Statistical Methods in Medical Research, 23(3), 308–311.
Nagaraj, N. (1990). Two-sided tests for change in level for correlated data. Statistical Papers, 31, 181–194.
Nelsen, R. B. (2006). An Introduction to Copulas. Springer.
Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41, 100–115.
Pastor, R., & Guallar, E. (1998). Use of two-segmented logistic regression to estimate change-points in epidemiologic studies. American Journal of Epidemiology , 148 (7), 631–642.
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.
Reeves, J., Chen, J., Wang, X. L., Lund, R., & Lu, Q. Q. (2007). A review and comparison of changepoint detection techniques for climate data. Journal of Applied Meteorology and Climatology, 46(6), 900–915.
Sklar, M. (1959). Fonctions de r ́epartition `a n dimensions et leurs marges. In Annales de l’isup (Vol. 8, pp. 229–231).
Yu, X., Baron, M., & Choudhary, P. K. (2013). Change-point detection in binomial thinning processes, with applications in epidemiology. Sequential Analysis, 32(3), 350– 367.

指導教授

孫立憲(Li-Hsien Sun)

審核日期

2024-7-26

推文