Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Ramadha Piyadi Gamage.pdf (837.87 KB)

ETD Abstract Container

Abstract Header

Empirical Likelihood For Change Point Detection And Estimation In Time Series Models

Piyadi Gamage, Ramadha D
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1495457528719879

Abstract Details

2017, Doctor of Philosophy (Ph.D.), Bowling Green State University, Statistics.
Empirical Likelihood (EL) method introduced by Owen (1988) is a widely used nonparametric tool for constructing confidence regions due to its appealing asymptotic distribution of the likelihood-ratio-type statistic which is same as the one under the parametric settings. However, the EL method was introduced to be used for independent data, hence it becomes difficult to apply it to dependent data such as time series data. Owen (2001) suggested using the conditional likelihood to remove the dependence structure and generate the estimating equations. Monti (1997) developed the idea of extending the EL method to short-memory time series models using the Whittle’s (1953) estimation method to obtain an M-estimator of the periodogram ordinates of a time series which are asymptotically independent. This reduces a dependent data problem into an independent data problem. Nordman and Lahiri (2006) also formulated a frequency domain empirical likelihood (FDEL) using spectral estimating equations which can be used for short- and long- range dependent data. FDEL applies a data transformation which weakens the dependence structure of the data hence, allowing to use the EL method for the transformed data which is considered to be asymptotically independent. Unfortunately, there is a good chance that the solution to the profile empirical likelihood function computation which involves constrained maximization does not exist which raises some computational issues as mentioned by Chen et al. (2008). To overcome this difficulty, Chen et al. (2008) proposed an adjusted empirical likelihood (AEL) ratio function by adding a pseudo term to guarantee the zero to be an interior point of the convex hull, therefore, the required numerical maximization is guaranteed to have a solution always. This dissertation focuses on developing novel nonparametric tests based on the empirical likelihood to estimate and detect changes in parameters of various times series models. First part is focused on the AEL for short-memory time series models such as autoregression (AR), moving average (MA), autoregressive moving average (ARMA), etc. I incorporated Monti’s (1997) approach along with Nordman and Lahiri’s (2006) formulation, to propose an AEL for short-memory dependence data. In the second part, an AEL-type statistic has been established for long-memory time series models suggested by Yau (2012). The third part of the dissertation focuses on the detection of changes in structures of time series models based on the EL method. Real data sets are used in each section to illustrate the performance of the proposed methods.
WEI NING (Committee Co-Chair)
ARJUN GUPTA (Committee Co-Chair)
JUNFENG SHANG (Committee Member)
ROBERT MIDDEN (Committee Member)
124 p.
Statistics
Nonparametric; Change point; Empirical Likelihood

Recommended Citations

Citations

  • Piyadi Gamage, R. D. (2017). Empirical Likelihood For Change Point Detection And Estimation In Time Series Models [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1495457528719879

    APA Style (7th edition)

  • Piyadi Gamage, Ramadha. Empirical Likelihood For Change Point Detection And Estimation In Time Series Models . 2017. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1495457528719879.

    MLA Style (8th edition)

  • Piyadi Gamage, Ramadha. "Empirical Likelihood For Change Point Detection And Estimation In Time Series Models ." Doctoral dissertation, Bowling Green State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1495457528719879

    Chicago Manual of Style (17th edition)

bgsu1495457528719879
722
© 2017, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.