Doctoral Dissertations


Xiao Zhong


"Unit root tests are frequently employed by applied time series analysts to determine if the underlying model that generates an empirical process has a component that can be well-described by a random walk. More specifically, when the time series can be modeled using an autoregressive moving average (ARMA) process, such tests aim to determine if the autoregressive (AR) polynomial has one or more unit roots. The effect of economic shocks do not diminish with time when there is one or more unit roots in the AR polynomial, whereas the contribution of shocks decay geometrically when all the roots are outside the unit circle. This is one major reason for economists' interest in unit root tests. Unit roots processes are also useful in modeling seasonal time series, where the autoregressive polynomial has a factor of the form (1-Zs), and s is the period of the season. Such roots are called seasonal unit roots. Techniques for testing the unit roots have been developed by many researchers since late 1970s. Most such tests assume that the errors (shocks) are independent or weakly dependent. Only a few tests allow conditionally heteroskedastic error structures, such as Generalized Autoregressive Conditionally Heteroskedastic (GARCH) error. And only a single test is available for testing multiple unit roots. In this dissertation, three papers are presented. Paper I deals with developing bootstrap-based tests for multiple unit roots; Paper II extends a bootstrap-based unit root test to higher order autoregressive process with conditionally heteroscedastic error; and Paper III extends a currently available seasonal unit root test to a bootstrap-based one while at the same time relaxing the assumption of weakly dependent shocks to include conditional heteroscedasticity in the error structure"--Abstract, page iv.


Samaranayake, V. A.

Committee Member(s)

Paige, Robert
Adekpedjou, Akim
Olbricht, Gayla R.
Gelles, Gregory M.


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics and Statistics


Ph. D. in Mathematics with emphasis in Statistics


Missouri University of Science and Technology

Publication Date

Fall 2015

Journal article titles appearing in thesis/dissertation

  • A bootstrap-based test for multiple unit roots
  • Bootstrap-based unit root tests for higher order auto-regressive models with GARCH(1,1) errors
  • Bootstrap-based unit root testing for seasonal time series under GARCH(1,1) errors


ix, 114 pages

Note about bibliography

Includes bibliographic references.


© 2015 Xiao Zhong, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Time-series analysis
Autoregression (Statistics)
Bootstrap (Statistics)

Thesis Number

T 10840

Electronic OCLC #