Maximum Likelihood Estimation of Autoregressive Models with a Near Unit Root and Cauchy Errors
- 주제(키워드) near unit root , Cauchy errors , maximum likelihood estimator , infinite variance
- 발행기관 서강대학교 일반대학원
- 지도교수 최인
- 발행년도 2016
- 학위수여년월 2016. 8
- 학위명 석사
- 학과 및 전공 일반대학원 경제학과
- 실제URI http://www.dcollection.net/handler/sogang/000000060014
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
This paper studies maximum likelihood estimation of autoregressive models with a near unit root and Cauchy errors. The maximum likelihood estimator (MLE) for the autoregressive coefficient is n^{3/2}-consistent with n denoting the sample size and converges in distribution to a random variable involving Cauchy and Gaussian processes. The MLE for the scale parameter of Cauchy distribution has the conventional √n-convergence and is asymptotically normal. The MLEs of the intercept and the linear time trend are n^{1/2} and n^{3/2}-consistent respectively. It is also shown that the t-test for a unit root based on the MLE is asymptotically standard normal. In addition, the finite sample properties of MLE are compared with those of the least square estimator (LSE). It is found that the MLE is more efficient than the LSE when the errors have a Cauchy distribution or a distribution which is slightly different from Cauchy. It is shown that the empirical power of t-test based on MLE is much larger than that of Dickey Fuller t-test.
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