Limit Theory for Moderate Deviations from a Unit Root Under Innovations with a Possibly Infinite Variance
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- 作者：Sai-Hua Huang (1)
Tian-Xiao Pang (2)
Chengguo Weng (3) - 关键词：Unit root process ; Moderate deviation ; Convergence rate ; Limiting distribution ; 62F12 ; 60F05
- 刊名：Methodology and Computing in Applied Probability
- 出版年：2014
- 出版时间：March 2014
- 年：2014
- 卷：16
- 期：1
- 页码：187-206
- 全文大小：498 KB
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10. White JS (1958) The limiting distribution of the serial correlation coefficient in the explosive case. Ann Math Stat 29:1188鈥?197 CrossRef - 作者单位：Sai-Hua Huang (1)
Tian-Xiao Pang (2)
Chengguo Weng (3)
1. Department of Ocean Science and Engineering, Zhejiang University, Zijingang Campus, Hangzhou, 310058, People鈥檚 Republic of China
2. Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People鈥檚 Republic of China
3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1, Canada - ISSN：1573-7713
文摘
An asymptotic theory was given by Phillips and Magdalinos (J Econom 136(1):115鈥?30, 2007) for autoregressive time series Y t 鈥?鈥?em class="a-plus-plus">蟻Y t鈭?鈥?鈥?em class="a-plus-plus">u t , t鈥?鈥?,...,n, with 蟻鈥?鈥?em class="a-plus-plus">蟻 n 鈥?鈥?鈥?鈥?em class="a-plus-plus">c/k n , under (2鈥?鈥?em class="a-plus-plus">未)-order moment condition for the innovations u t , where 未鈥?gt;鈥? when c鈥?lt;鈥? and 未鈥?鈥? when c鈥?gt;鈥?, {u t } is a sequence of independent and identically distributed random variables, and (k n ) n鈥夆垐鈥夆剷 is a deterministic sequence increasing to infinity at a rate slower than n. In the present paper, we established similar results when the truncated second moment of the innovations $l(x)=\textsf{E} [u_1^2I\{|u_1|\le x\}]$ is a slowly varying function at 鈭? which may tend to infinity as x鈥夆啋鈥夆垶. More interestingly, we proposed a new pivotal for the coefficient 蟻 in case c鈥?lt;鈥?, and formally proved that it has an asymptotically standard normal distribution and is nuisance parameter free. Our numerical simulation results show that the distribution of this pivotal approximates the standard normal distribution well under normal innovations.