具有高斯创新的AR(1)和MA(1)过程中大偏差的显式二元速率函数

IF 1 2区 数学 Q3 STATISTICS & PROBABILITY
M. J. Karling, A. Lopes, S. Lopes
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引用次数: 1

摘要

我们通过给出随机向量序列$(\boldsymbol{S}_n)_{n \in \N} = \left(n^{-1}(\sum_{k=1}^n X_k, \sum_{k=1}^n X_k^2)\right)_{n \in \N}$的显式二元速率函数,研究了具有独立高斯创新的中心平稳AR(1)和MA(1)过程的大偏差特性。在AR(1)的情况下,我们也给出了二元随机序列$(\W_n)_{n \geq 2} = \left(n^{-1}(\sum_{k=1}^n X_k^2, \sum_{k=2}^n X_k X_{k+1})\right)_{n \geq 2}$的显式速率函数。通过收缩原理,我们还为序列$(n^{-1} \sum_{k=1}^n X_k)_{n \in \N}$、$(n^{-1} \sum_{k=1}^n X_k^2)_{n \geq 2}$和$(n^{-1} \sum_{k=2}^n X_k X_{k+1})_{n \geq 2}$提供了显式的速率函数。在AR(1)情况下,我们对Yule-Walker估计量的显式偏差函数的已知结果给出了新的证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Explicit bivariate rate functions for large deviations in AR(1) and MA(1) processes with Gaussian innovations
We investigate large deviations properties for centered stationary AR(1) and MA(1) processes with independent Gaussian innovations, by giving the explicit bivariate rate functions for the sequence of random vectors $(\boldsymbol{S}_n)_{n \in \N} = \left(n^{-1}(\sum_{k=1}^n X_k, \sum_{k=1}^n X_k^2)\right)_{n \in \N}$. In the AR(1) case, we also give the explicit rate function for the bivariate random sequence $(\W_n)_{n \geq 2} = \left(n^{-1}(\sum_{k=1}^n X_k^2, \sum_{k=2}^n X_k X_{k+1})\right)_{n \geq 2}$. Via Contraction Principle, we provide explicit rate functions for the sequences $(n^{-1} \sum_{k=1}^n X_k)_{n \in \N}$, $(n^{-1} \sum_{k=1}^n X_k^2)_{n \geq 2}$ and $(n^{-1} \sum_{k=2}^n X_k X_{k+1})_{n \geq 2}$, as well. In the AR(1) case, we present a new proof for an already known result on the explicit deviation function for the Yule-Walker estimator.
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来源期刊
CiteScore
1.60
自引率
13.30%
发文量
29
审稿时长
12 weeks
期刊介绍: Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1). Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.
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