本文論述了一種全新的快速探測時間序列中結構性突變點的過程。我們應用了一個新的統計量，平均時間常方差，作為樣本協方差結構改變的代理變量。平均時間常方差也可以表現為所有協方差函數的和。吳(2009)提出了一種能夠遞歸計算平均時間常方差估計值的算法並被我們應用在這篇文，其有效更新計算及記憶複雜度均為O(1) 。在這篇文章中，我們研究了平均時間常方差估計值的漸進分佈並設立了一組置信帶(confidence bands) 來監視時間序列是否有突變發生。根據蒙特卡洛模擬，我們發現這種測試方法有很好的統計特性規模(size) 和檢驗力(power)。微陣列數據(Microarray data) 的實例在我們的文章中也進行了展示。我們的算法只在1. 86GHz的處理器中，需要約2秒就能夠檢測長度為10000 的序列。 / This paper proposes a new and fast change point detection procedure for time series. We develop a new proxy for the change in the (sample) covariance structure, the Time Average Variance Constant (TAVC), which could be expressed as the summation of all the auto-covariance functions. Wu (2009)'s algorithm is implemented to compute the estimate of TAVC recursively with an efficient updating computational and memory complexity of O(1). In this article, we study an asymptotic distribution of TAVC estimator and construct condence bands to monitor whether a change happens in a time series. We show the good size and power properties of the procedure based on Monte Carlo Simulation. Illustrations using microarray data are presented. Our algorithm only takes~2s on a single 1.86GHz processor with a sequence of length 10,000. / Detailed summary in vernacular field only. / Jin, Yong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 38-45). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Time Average Variance Constant --- p.6 / Chapter 2.1 --- What is Time Average Variance Constant? --- p.6 / Chapter 2.2 --- Another Look at TAVC --- p.7 / Chapter 2.3 --- Estimation of Time Average Variance Constant --- p.7 / Chapter 2.3.1 --- Algorithm 1: Wu(2009) --- p.8 / Chapter 2.3.2 --- Algorithm 2: Wu(2009) --- p.8 / Chapter 3 --- Behavior of the Sample Auto-Covariance Structure for a Change in Mean --- p.11 / Chapter 3.1 --- Problem Formulation --- p.11 / Chapter 3.2 --- CUSUM Test --- p.12 / Chapter 3.3 --- Behavior of the Sample Auto-Covariance Structure --- p.14 / Chapter 4 --- Change-Point Tests and Algorithms --- p.17 / Chapter 4.1 --- Asymptotic Normality --- p.17 / Chapter 4.2 --- A Change Point Detection Procedure based on TAVC --- p.22 / Chapter 4.2.1 --- Algorithm 3 --- p.23 / Chapter 4.2.2 --- An example: AR(1) Model with p = 0.4 --- p.24 / Chapter 4.2.3 --- Size And Power --- p.26 / Chapter 4.3 --- Array CGH data Example --- p.28 / Chapter 5 --- Conclusion --- p.31 / Chapter 6 --- Appendix --- p.32 / Chapter 6.1 --- Proof of Theorem 3.1 --- p.32 / Bibliography --- p.38
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328000 |
| Date | January 2012 |
| Contributors | Jin, Yong., Chinese University of Hong Kong Graduate School. Division of Risk Management Science. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (v, 45 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
Page generated in 0.0016 seconds