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 $c \rightarrow \infty$.
Publié le : 1982-08-14
Classification:
Autoregression,
maximum term,
Pareto,
exponential,
first passage time,
asymptotic distribution,
60G10,
60G40,
60G50,
60F99
@article{1176993781,
author = {Finster, Mark},
title = {The Maximum Term and First Passage Times for Autoregressions},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 737-744},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993781}
}
Finster, Mark. The Maximum Term and First Passage Times for Autoregressions. Ann. Probab., Tome 10 (1982) no. 4, pp. 737-744. http://gdmltest.u-ga.fr/item/1176993781/