Abstract
We consider a nearly unstable, or near unit root, AR(1) process with regularly varying innovations. Two different approximations for the stationary distribution of such processes exist: a Gaussian approximation arising from the nearly unstable nature of the process and a heavy-tail approximation related to the tail asymptotics of the innovations. We combine these two approximations to obtain a new uniform approximation that is valid on the entire real line. As a corollary, we obtain a precise description of the regions where each of the Gaussian and heavy-tail approximations should be used.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference25 articles.
1. [8] Cline D. (1983). Estimation and linear prediction for regression, autoregression and arma with infinite variance data. Doctoral Thesis, Colorado State University.
2. Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications;Barbe;Mem. Amer. Math. Soc.,2009
3. Recurrence properties of autoregressive processes with super-heavy-tailed innovations
4. The supremum of a negative drift random walk with dependent heavy-tailed steps;Mikosch;Ann. Appl. Prob.,2000
5. Weak convergence of an autoregressive process used in modeling population growth
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献