NDLI: The limit theorem for dependent random variables with applications to autoregression models

Content Provider	Springer Nature Link
Author	Zhang, Yong Yang, Xiaoyun Dong, Zhishan Wang, Dehui
Copyright Year	2011
Abstract	This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {X $_{ t }$} be a linear process defined by X $_{ t }$ = Σ k=0 ∞ ψ$_{ k }$ ɛ $_{ t−k }$, where {ψ$_{ k }$, k ≥ 0} is a sequence of real numbers and {ɛ $_{ k }$, k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {ɛ $_{ k }$, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter α when {ɛ $_{ k }$, k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ $_{0}$ = 1, ψ $_{ k }$ = 0, k ≥ 1.
Starting Page	565
Ending Page	579
Page Count	15
File Format	PDF
ISSN	10096124
Journal	Journal of Systems Science and Complexity
Volume Number	24
Issue Number	3
e-ISSN	15597067
Language	English
Publisher	Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Publisher Date	2011-06-14
Publisher Place	Beijing
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ALNQD autoregression models least squares estimator negatively associated unit root test Statistics Statistical Physics, Dynamical Systems and Complexity Operations Research/Decision Theory Mathematics of Computing Systems Theory, Control
Content Type	Text
Resource Type	Article
Subject	Information Systems

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