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August, 1982 The Maximum Term and First Passage Times for Autoregressions
Mark Finster
Ann. Probab. 10(3): 737-744 (August, 1982). DOI: 10.1214/aop/1176993781


The limiting distribution of the maximum term of the non-normal stationary sequence $\cdots X_{-1}, X_0, X_1 \cdots$ satisfying the autoregressive equation $X_n = \varepsilon_n + a_1X_{n-1} + a_2X_{n-2} + \cdots$ is investigated when $\sum |a_k| < 1$ and $\cdots \varepsilon_{-1}, \varepsilon_0, \varepsilon_1 \cdots$ are integrable real valued i.i.d. random variables having distributions with tails that are either Pareto or exponential in nature. Asymptotic results for the joint distribution of the first passage time $t = \inf\{n: X_n \geq c\}$ and the excess $R_t = X_t - c$ are also given as $c \rightarrow \infty$.


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Mark Finster. "The Maximum Term and First Passage Times for Autoregressions." Ann. Probab. 10 (3) 737 - 744, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0493.60049
MathSciNet: MR659542
Digital Object Identifier: 10.1214/aop/1176993781

Primary: 60G10
Secondary: 60F99 , 60G40 , 60G50

Keywords: asymptotic distribution , Autoregression , exponential , First passage time , maximum term , Pareto

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
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