A robust test for threshold-type non-linearity in bivariate time series analysis.

• Other Authors: Chow, Wai Kit.
• Format: Others
• Language: English; Chinese
• Published: 2012
• Subjects: Time-series analysis > Mathematical models; Nonlinear theories
• Online Access: http://library.cuhk.edu.hk/record=b5549036; http://repository.lib.cuhk.edu.hk/en/item/cuhk-328572

在實際分析數據的時候,我們經常遇到二元時間序列數據。在許多情況下，由於普通線性二元時間序列模型未必足以說明較複雜的社會和自然現象，許多分析家認為，多元非線性時間序列模型可以提供一個可行的解決方案。在許多不同類型的多元非線性時間序列中，一個重要的類別是二元門限自回歸（BTAR）模型。BTAR 模型可以充分捕到時間序列數據中的極限週期跳躍現象及振幅頻率。Tsay (1998) [37] 提出了多元的門限型的非線性檢驗。然而，這種檢驗對被異常點污染了的時間序列數據的表現不太令人滿意。為了糾正Tsay (1998) [37]檢驗的缺點，我們提出一個穩健的檢驗程序。本論文的重點是二元時間序列數據。重新加權二元最小消平方法被採用從而推出一個穩健的門限型非線性檢驗。亦得出該檢驗的統計量在原假設下的漸近分怖。透過模擬實驗,找出提出的檢驗的性能，並且與根據最小消平方法建立的Tsay (1998) [37]的檢驗作出比較，我們也會提供實際的數據例子給予說明。 === Bivariate time series data are frequently encountered in practical situations. In many cases, since ordinary linear bivariate time series models may not be sufficient to de-scribe complex social and natural phenomena, many analysts believe that vector non-linear time series models could provide a viable solution. Among many different types of vector non-linear time series processes, an important class is the bivariate threshold autoregressive (BTAR) model. BTAR model can be employed to capture limit cycles, jump phenomenon and amplitude-frequency in the time series data. A test for threshold-type non-linearity in a vector time series was proposed by Tsay (1998) [38]. However, this test does not perform satisfactorily if the data are contaminated by outliers. To remedy the drawback of the Tsay' s (1998) [38] test, we propose a robust testing procedure. The focus of this thesis is on bivariate time series data. The reweighted bivariate least trimmed squares method is adopted to derive a robust test for threshold-type non-linearity. The asymptotic null distribution of the proposed test statistic is dervied. Simulation studies are conducted to investigate the performance of the proposed test and to compare it with the least squares method based on the Tsay's (1998) [38] test. Numerical examples are provided for illustrative purposes. === Detailed summary in vernacular field only. === Chow, Wai Kit. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. === Includes bibliographical references (leaves 40-44). === Abstracts also in Chinese. === Abstract --- p.i === Acknowledgement --- p.iii === Chapter 1 --- Introduction --- p.1 === Chapter 1.1 --- Linear Time Series Models and Their Applications --- p.1 === Chapter 1.2 --- Non-linear Time Series Models and Their Applications --- p.3 === Chapter 1.3 --- Threshold Autoregressive Model (TAR) and the Self-exciting Threshold Autoregressive Model (SETAR) --- p.4 === Chapter 1.4 --- Outliers in Univariate Time Series --- p.5 === Chapter 1.5 --- Bivariate Autoregressive Model (BAR) --- p.6 === Chapter 1.6 --- Bivariate Threshold Autoregressive Model (BTAR) --- p.7 === Chapter 1.7 --- Outliers in Bivariate Time Series --- p.8 === Chapter 1.8 --- Objectives of the Thesis --- p.9 === Chapter 1.9 --- Organisation of the Thesis --- p.10 === Chapter 2 --- The Proposed Test --- p.11 === Chapter 2.1 --- Tsay's Test --- p.11 === Chapter 2.2 --- Reweighted Multivariate Least Trimmed Squares Method --- p.14 === Chapter 2.3 --- The Proposed Test --- p.18 === Chapter 3 --- Simulation Study --- p.24 === Chapter 3.1 --- Under the Null Hypothesis --- p.24 === Chapter 3.2 --- Under the Alternative Hypothesis --- p.26 === Chapter 3.3 --- The Choice of γ and δ --- p.28 === Chapter 4 --- Examples --- p.31 === Chapter 4.1 --- Simulated Data --- p.31 === Chapter 4.2 --- Gas-Furnace Data --- p.33 === Chapter 4.3 --- Blowfly Data --- p.35 === Chapter 5 --- Conclusions and Further Research --- p.38 === Bibliography --- p.40