scholarly journals MULTIVARIATE LIMIT THEOREMS IN THE CONTEXT OF LONG-RANGE DEPENDENCE

2013 ◽  
Vol 34 (6) ◽  
pp. 717-743 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Range ◽  
Limit Theorems ◽  
Long Range Dependence

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

scholarly journals Ordinal Pattern Dependence in the Context of Long-Range Dependence

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 670
Author(s):  
Ines Nüßgen ◽  
Alexander Schnurr
Keyword(s):  
Time Series ◽  
Long Range ◽  
Limit Theorems ◽  
Long Range Dependence ◽  
Limit Distributions ◽  
Ordinal Information ◽  
Dependence Measure ◽  
Multivariate Dependence ◽  
Ordinal Time Series ◽  
Ordinal Pattern

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for a long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators of ordinal pattern dependence. In doing so, we point out the differences that arise for the underlying time series having different dependence structures. Depending on these assumptions, central and non-central limit theorems are proven. The limit distributions for the latter ones can be included in the class of multivariate Rosenblatt processes. Finally, a simulation study is provided to illustrate our theoretical findings.

scholarly journals Long range dependence of heavy-tailed random functions

2021 ◽  
Vol 58 (3) ◽  
pp. 569-593
Author(s):  
Rafal Kulik ◽  
Evgeny Spodarev
Keyword(s):  
Long Range ◽  
Random Function ◽  
Limit Theorems ◽  
Random Processes ◽  
Long Range Dependence ◽  
Infinite Variance ◽  
Random Functions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Index Space

AbstractWe introduce a definition of long range dependence of random processes and fields on an (unbounded) index space $T\subseteq \mathbb{R}^d$ in terms of integrability of the covariance of indicators that a random function exceeds any given level. This definition is specifically designed to cover the case of random functions with infinite variance. We show the value of this new definition and its connection to limit theorems via some examples including subordinated Gaussian as well as random volatility fields and time series.

Central limit theorems for nearly long range dependent subordinated linear processes

2020 ◽  
Vol 57 (2) ◽  
pp. 637-656
Author(s):  
Martin Wendler ◽  
Wei Biao Wu
Keyword(s):  
Long Range ◽  
Central Limit ◽  
Short Range ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Partial Sums ◽  
Long Range Dependence ◽  
Stationary Sequences ◽  
Linear Processes ◽  
Arbitrary Power

AbstractThe limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

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