Bootstrapping Unit Root Tests for MA(1) Processes

• Main Authors: Hsin-Yu Ho, 何心瑀
• Other Authors: Nan-Jung Hsu
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/74778489028790775158

碩士 === 國立清華大學 === 統計學研究所 === 95 === Four new bootstrap tests for testing unit root in the moving average model of order one (MA(1)) are proposed in this thesis. The four bootstrap tests are the test without restriction under Gaussian (i.e., the test which is based on the least square estimator and is not imposed the null hypothesis), the test with restriction under Gaussian (i.e., which is the test based on the least square estimator and is imposed the null hypothesis), the test without restriction under Laplace, (i.e., the test which is based on the least absolute deviation (LAD) estimator and is not imposed the null hypothesis), and last, the test with restriction under Laplace (i.e., the test which is based on the LAD estimator and is imposed the null hypothesis). Besides, we compare the performance among these tests in terms of the power and size under four different error distributions by simulation. It shows that under Gaussian estimation, the performance is no difference whether we impose the null hypothesis or not. However, under Laplace estimation, the test without restriction is more powerful than the test with restriction. It also shows that when the distribution of the error term has a heavy tail, the tests under Laplace outperform the tests under Gaussian.