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

Content Provider	Springer Nature Link
Author	Owada, Takashi
Copyright Year	2014
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.
Ending Page	95
Page Count	33
Starting Page	63
File Format	PDF
ISSN	08949840
e-ISSN	15729230
Journal	Journal of Theoretical Probability
Issue Number	1
Volume Number	29
Language	English
Publisher	Springer US
Publisher Date	2014-07-03
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Time series, auto-correlation, regression, etc. Stationary processes Heavy tails Probability Theory and Stochastic Processes Statistics Infinitely divisible process Nonsingular (and infinite-measure preserving) transformations Conservative flow Darling–Kac theorem Sample autocovariance Stable processes Central limit and other weak theorems Pointwise dual ergodicity
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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

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

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