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研究生:王耀霆
研究生(外文):Yao-Ting, Wang
論文名稱:單改變點自我相關條件卜松分配之貝式推論
論文名稱(外文):Bayesain Estimation of ACP(1,1) with a Change point
指導教授:陳婉淑
指導教授(外文):Cathy W.S. Chen
口試委員:林彩玉許英麟
口試日期:2014-07-14
學位類別:碩士
校院名稱:逢甲大學
系所名稱:統計學系統計與精算碩士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:52
中文關鍵詞:計數型資料改變點過度離散馬可夫鏈蒙地卡羅貝氏診斷分析
外文關鍵詞:Time series of countAutoregressive Conditional PoissonOver-dispersionBayesian diagnostic checkingMCMC
相關次數:
  • 被引用被引用:0
  • 點閱點閱:188
  • 評分評分:
  • 下載下載:14
  • 收藏至我的研究室書目清單書目收藏:0
計數型時間序列經常伴隨著結構性改變。本篇論文主要分為兩個部分:首先,回顧對於整數型時間序列模型的發展。其次,我們提出自我相關條件卜松分配 (ACP) 在單一改變點 (change point) 透過貝式估計方法。這種未知改變點在自我相關條件卜松分配,允許在改變點前後具有不對稱性的非條件平均數。本研究在貝氏架構下,使用馬可夫鏈蒙地卡羅法對參數和改變點估計。本論文採用事後眾數估計改變點,因為改變點的發生是在一個整數型時間點之下。在貝氏方法的範疇之下我們提出一個應用重點抽樣的診斷分析方法估計一般化的殘差,判斷所用模式是否合適,並結合貝氏估計方法。我們使用模擬研究,檢視在單一改變點之下自我相關條件卜松分配的估計表現。為了闡明所提出的方法,我們考慮簡單的ACP(1,1)和在單一改變點之下的ACP(1,1),分析三組澳大利亞新南威爾斯省的犯罪資料。我們採用Ljung-Box 檢定和常態檢定,檢查對於所提出的模型是否合適。診斷分析結果顯示,分析的三組資料並沒有不合適的指標。
Structural change can happen in a time series of counts. The goal of this paper has two fields. First, we review the development of integer-valued time series models. Second, we propose autoregressive conditional Poisson (ACP) models with a change point via a Bayesian approach. This change point is unknown in the ACP model, which allows asymmetric unconditional mean in the two time spans. Bayesian MCMC methods are used to estimate parameters simultaneously in the mean process and the change point. The change point is estimated by a posterior mode since it is an integer value. We also propose a diagnostic checking based on important sampling method which is within a Bayesian approach. We conduct a simulation study to investigate the estimation performance of ACP model with a change point. In order to illustrate the proposed method, three real data sets are considered, in which the ACP model and ACP model with a change point are applied to the crime data sets in Australia. We apply the Ljung-Box test and normality tests to check the generalized residuals whether the proposed model is adequacy. The diagnostic checking result show that there is no sign of inadequacy in all three data series.
1 Introduction 4
2 ACP model with a change point 9
3 Bayesian Inference 10
4 MCMC sampling scheme 12
5 Diagnostic checking 14
6 Simulation study 15
7 Empirical study 30
8 Conclusion and Future Works 48
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