Limit Theory for Moderate Deviations from a Unit Root Under Innovations with a Possibly Infinite Variance

Sai-Hua Huang (), Tian-Xiao Pang () and Chengguo Weng ()
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Sai-Hua Huang: Zhejiang University
Tian-Xiao Pang: Zhejiang University
Chengguo Weng: University of Waterloo

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 1, 187-206

Abstract: Abstract An asymptotic theory was given by Phillips and Magdalinos (J Econom 136(1):115–130, 2007) for autoregressive time series Y t = ρY t−1 + u t , t = 1,...,n, with ρ = ρ n = 1 + c/k n , under (2 + δ)-order moment condition for the innovations u t , where δ > 0 when c 0, {u t } is a sequence of independent and identically distributed random variables, and (k n ) n ∈ ℕ 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 ∞, which may tend to infinity as x → ∞. More interestingly, we proposed a new pivotal for the coefficient ρ in case c

Keywords: Unit root process; Moderate deviation; Convergence rate; Limiting distribution; 62F12; 60F05 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-012-9306-7

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