One of the essential features of financial time series data is volatility. It is often the case that, over time, structural changes occur in volatility, and an accurate estimation of the volatility of financial time series requires careful identification of the change-points. A common approach to modeling the volatility of time series data is based on the well-known Generalized Autoregressive Conditional Heteroscedastic (GARCH) model. Although the problem of change-point estimation of volatility dynamics derived from the GARCH model has been considered in the literature, these approaches rely on parametric assumptions of the conditional error distribution, which are frequently violated in financial time series. This misspecification of error distribution may lead to change-point detection inaccuracies, resulting in unreliable GARCH volatility estimates. In this dissertation, we introduce novel change-point detection algorithms based on a semiparametric GARCH model. The proposed semiparametric GARCH model retains the structural advantages of the GARCH process while incorporating the flexibility of nonparametric conditional error distribution. Consequently, the likelihood function and the corresponding volatility estimates obtained via this semiparametric approach are more accurate than the traditional Quasi-Maximum Likelihood Estimation (QMLE) method that relies on an assumed parametric error distribution. The main objective of the change-point estimation problem is to detect the exact number and locations of the change-points. This dissertation proposes an innovative semiparametric GARCH process in developing solutions for change-point estimation problems. Specifically, a penalized likelihood approach based on a semiparametric GARCH model and an efficient binary segmentation algorithm is developed to estimate the change points' locations. The results demonstrate that in terms of change-point identification and estimation accuracy for multiple GARCH process variations, the proposed semiparametric method outperforms the commonly used approaches to change-point analysis in financial data.

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Since the introduction of CUSUM statistic by E.S. Page (1951), detection of change or a structural break in time series has gained significant interest as its applications span across various disciplines including economics, industrial applications, and environmental data sets. However, many of the early suggested statistics, such as CUSUM or MOSUM, lose their effectiveness when applied to time series data. Either the size or power of the test statistic gets distorted, especially for higher order autoregressive moving average processes. We use the test statistic from Gombay and Serban (2009) for detecting change in the mean of an autoregressive process and show how the application of sieve bootstrap to the time series data can improve the performance of our test to detect change. The effectiveness of the proposed method is illustrated by applying it to economic data sets.

Since the introduction of CUSUM statistic by E.S. Page (1951), detection of change or a structural break in time series has gained significant interest as its applications span across various disciplines including economics, industrial applications, and environmental data sets. However, many of the early suggested statistics, such as CUSUM or MOSUM, lose their effectiveness when applied to time series data. Either the size or power of the test statistic gets distorted, especially for higher order autoregressive moving average processes. We use the test statistic from Gombay and Serban (2009) for detecting change in the mean of an autoregressive process and show how the application of sieve bootstrap to the time series data can improve the performance of our test to detect change. The effectiveness of the proposed method is illustrated by applying it to economic data sets.

The adoption of cloud computing has increased dramatically in recent years due to at- tractive features such as flexibility, cost reductions, scalability, and pay per use. Shifting towards cloud computing is attracting not only industry but also government and academia. However, given their stringent privacy and security policies, this shift is still hindered by many security concerns related to the cloud computing features, namely shared resources, virtualization and multi-tenancy. These security concerns vary from privacy threats and lack of transparency to intrusions from within and outside the cloud infrastructure. There- fore, to overcome these concerns and establish a strong trust in cloud computing, there is a need to develop adequate security mechanisms for effectively handling the threats faced in the cloud. Intrusion Detection Systems (IDSs) represent an important part of such mech- anisms. Developing cloud based IDS that can capture suspicious activity or threats, and prevent attacks and data leakage from both inside and outside the cloud environment is paramount. However, cloud computing is faced with a multidimensional and rapidly evolv- ing threat landscape, which makes cloud based IDS more challenging. Moreover, one of the most significant hurdles for developing such cloud IDS is the lack of publicly available datasets collected from a real cloud computing environment. In this dissertation, we intro- duce the first public dataset of its kind, named ISOT Cloud Intrusion Dataset (ISOT-CID), for cloud intrusion detection. The dataset consists of several terabytes of data, involving normal activities and a wide variety of attack vectors, collected over multiple phases and periods of time in a real cloud environment. We also introduce a new hypervisor-based cloud intrusion detection system (HIDS) that uses online multivariate statistical change analysis to detect anomalous network behaviors. As a departure from the conventional monolithic network IDS feature model, we leverage the fact that a hypervisor consists of a collection of instances, to introduce an instance-oriented feature model that exploits indi- vidual as well as correlated behaviors of instances to improve the detection capability. The proposed approach is evaluated using ISOT-CID and the experiments along with results are presented. / Graduate / 2020-08-14

For a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a non-parametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error distributions. Under the alternative hypothesis with a change-point, the comparisons with two other methods (Chen's SIC method and Muggeo's SEG method) show that the proposed method performs better when the slope change is small. A power analysis is conducted to illustrate the performance of the test. The proposed method is also applied to analyze two real datasets: the plasma osmolality dataset and the gasoline price dataset. / by Zhihua Liu. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 200?. Mode of access: World Wide Web.

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

Statistical inference in time series analysis has been an important subject in various fields including climate science, economics, finance and industrial engineering among others. Numerous problems of research interest include statistical inference about unknown quantities, assessing structural stability and forecasting. These problems have been widely studied in the literature, but mainly for independent data, while in many applications involving time series data dependence is not unusual and in fact quite common. In this thesis, we incorporate serial dependence into the analysis by involving self-normalization in time series analysis. We start with the problem of testing whether there are change-points in a given time series. The method we propose does not require the number of change-points to be predefined, and thus is unsupervised. It does not require any tuning parameters and can be applied to a wide class to quantities of interest. The asymptotic distribution of the test statistic is studied and an approximation scheme is proposed to reduce testing procedure complexity. We then consider the problem of construction of confidence intervals, for which the conventional self-normalizer exhibits certain degrees of asymmetry when applied to quantities other than the mean. The method we propose provides a time-symmetric generalization to the conventional self-normalizer and leads to improved finite sample performance for quantities other than the mean.

時間序列之變點鬥檻模型是一種非線性的模型。此論文探討有關該模型之參數估計，同時對其參數估計作出統計分析。我們運用了遺傳式計算機運算來估計這些參數及對其作出研究。我們利用了MDL來對比不同的變點門檻模型，同時我們也利用了MDL來選取對應的變點門檻模型。 / This article considers the problem of modeling non-linear time series by using piece-wise TAR model. The numbers of change points, the numbers of thresholds and the corresponding order of AR in each piecewise TAR segments are assumed unknown. The goal is to nd out the “best“ combination of the number of change points, the value of threshold in each time segment, and the underlying AR order for each threshold regime. A genetic algorithm is implemented to solve this optimization problem and the minimum description length principle is applied to compare various segmented TAR. We also show the consistency of the minimal MDL model selection procedure under general regularity conditions on the likelihood function. / Detailed summary in vernacular field only. / Tang, Chong Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 45-47). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 2 --- Minimum Description Length for Pure TAR --- p.4 / Chapter 2.1 --- Model selection using Minimum Description Length for Pure TAR --- p.4 / Chapter 2.1.1 --- Derivation of Minimum Description Length for Pure TAR --- p.5 / Chapter 2.2 --- Optimization Using Genetic Algorithms (GA) --- p.7 / Chapter 2.2.1 --- General Description --- p.7 / Chapter 2.2.2 --- Implementation Details --- p.9 / Chapter 3 --- Minimum Description Length for TAR models with structural change --- p.13 / Chapter 3.1 --- Model selection using Minimum Description Length for TAR models with structural change --- p.13 / Chapter 3.1.1 --- Derivation of Minimum Description Length for TAR models with structural change --- p.14 / Chapter 3.2 --- Optimization Using Genetic Algorithms --- p.17 / Chapter 4 --- Main Result --- p.20 / Chapter 4.1 --- Main results --- p.20 / Chapter 4.1.1 --- Model Selection using minimum description length --- p.21 / Chapter 5 --- Simulation Result --- p.24 / Chapter 5.1 --- Simulation results --- p.24 / Chapter 5.1.1 --- Example of TAR Model Without Structural Break --- p.24 / Chapter 5.1.2 --- Example of TAR Model With Structural Break I --- p.26 / Chapter 5.1.3 --- Example of TAR Model With Structural Break II --- p.29 / Chapter 6 --- An empirical example --- p.33 / Chapter 6.1 --- An empirical example --- p.33 / Chapter 7 --- Consistency of the CLSE --- p.36 / Chapter 7.1 --- Consistency of the TAR parameters --- p.36 / Chapter 7.1.1 --- Consistency of the estimation of number of threshold --- p.36 / Chapter 7.1.2 --- Consistency of the change point parameters --- p.43 / Bibliography --- p.45

Thesis (Ph. D.)--Carleton University, 2002. / Includes bibliographical references (p. 192-195). Also available in electronic format on the Internet.