Some limit theorems on stationary processes with long-range dependence

1996 ◽  
pp. 233-245 ◽  
Author(s):  
Yuzo Hosoya
Keyword(s):  
Long Range ◽  
Limit Theorems ◽  
Long Range Dependence ◽  
Stationary Processes

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 Estimation of marginal parameters of SUP-OU processes with long range dependence

2016 ◽  
Vol 4 (2) ◽  
pp. 102
Author(s):  
Emanuele Taufer
Keyword(s):  
Long Range ◽  
Asymptotic Theory ◽  
Marginal Distribution ◽  
Real Data ◽  
Function Technique ◽  
Long Range Dependence ◽  
Stationary Processes ◽  
Marginal Distributions ◽  
Non Gaussian ◽  
Basic Features

Superpositions of Ornstein Uhlenbeck processes provide convenient ways to build stationary processes with given marginal distributions and long range dependence. After reviewing some of the basic features, we present several examples of processes with non Gaussian marginal distributions. Estimation of the parameters of the marginal distribution is undertaken by means of a characteristic function technique. We provide the relevant asymptotic theory as well as results of simulations and real data applications.

On defining long-range dependence

1997 ◽  
Vol 34 (04) ◽  
pp. 939-944 ◽  
Author(s):  
C. C. Heyde ◽  
Y. Yang
Keyword(s):  
Long Range ◽  
Second Order ◽  
Long Range Dependence ◽  
Infinite Variance ◽  
Stationary Processes ◽  
Domain Of Applicability

Long-range dependence has usually been defined in terms of covariance properties relevant only to second-order stationary processes. Here we provide new definitions, almost equivalent to the original ones in that domain of applicability, which are useful for processes which may not be second-order stationary, or indeed have infinite variances. The ready applicability of this formulation for categorizing the behaviour for various infinite variance models is shown.

A power-law model and other models for long-range dependence

1997 ◽  
Vol 34 (3) ◽  
pp. 657-670 ◽  
Author(s):  
R. J. Martin ◽  
A. M. Walker
Keyword(s):  
Long Range ◽  
Discrete Time ◽  
Power Law ◽  
Long Range Dependence ◽  
Stationary Processes ◽  
Power Law Model ◽  
Slow Decay ◽  
Exact Power ◽  
Correlation Structures ◽  
Discrete Time Models

It is becoming increasingly recognized that some long series of data can be adequately and parsimoniously modelled by stationary processes with long-range dependence. Some new discrete-time models for long-range dependence or slow decay, defined by their correlation structures, are discussed. The exact power-law correlation structure is examined in detail.

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 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.

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