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Open Access Publications from the University of California

Bootstrap Tests for Unit Root and Seasonal Unit Root

  • Author(s): Zou, Nan
  • Advisor(s): Politis, Dimitris
  • et al.

Unit root process, as a process with stochastic trend and a generalization from random walk, is pervasive in physics, economics, and finance. In the hypothesis test for unit root, bootstrap methods have earned a great deal of attention. This dissertation proposes and investigates various bootstrap unit root tests. Chapter one applies linear process bootstrap to unit root test in order to alleviate the size distortions of unit root tests. While Chapter one focuses on classic unit root tests, which search for stochastic trend, Chapter two tackles seasonal unit root tests, which simultaneously check stochastic trend and stochastic seasonality. In addition, Chapter two takes into consideration seasonal heterogeneity, which pervades in seasonal processes. Specifically, Chapter two offers under seasonal heterogeneity a seasonal AR-sieve bootstrap remedy for a parametric seasonal unit root test and advocates a seasonal block bootstrap solution for a non-parametric test. This dissertation then establishes three bootstrap functional central limit theorems, via which this dissertation shows the consistency of all the aforementioned bootstrap methods.

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