Limit Theory for the Sample Autocovariance for Heavy-Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows

Takashi Owada ()
Additional contact information
Takashi Owada: Cornell University

Journal of Theoretical Probability, 2016, vol. 29, issue 1, 63-95

Abstract: Abstract This study aim to develop limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail marginals and is generated by a conservative flow. Interestingly, the growth rate of the sample autocovariances is determined not only by heavy tailedness of the marginals but also by the memory length of the process. Although this feature was first observed by Resnick et al. (Stoch Process Appl 85:321–339, 2000) for some very specific processes, we will propose a more general framework from the viewpoint of infinite ergodic theory. Consequently, the asymptotics of the sample autocovariances can be more comprehensively discussed.

Keywords: Infinitely divisible process; Heavy tails; Conservative flow; Pointwise dual ergodicity; Darling–Kac theorem; Sample autocovariance; Primary 60F05; 60G10; Secondary 37A40; 60G52; 62M10 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-014-0565-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:29:y:2016:i:1:d:10.1007_s10959-014-0565-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-014-0565-9

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().