Thoughts on the modelling and identification of random processes and fields subject to possible long-range dependence

2015 ◽  
Author(s):  
C. C. Heyde ◽  
Roger Gay
Keyword(s):  
Long Range ◽  
Random Processes ◽  
Long Range Dependence

scholarly journals Long range dependence for stable random processes

2020 ◽  
Author(s):  
Vitalii Makogin ◽  
Marco Oesting ◽  
Albert Rapp ◽  
Evgeny Spodarev
Keyword(s):  
Long Range ◽  
Random Processes ◽  
Long Range Dependence

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.

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 On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

Long range dependence in stock market returns

2006 ◽  
Vol 16 (18) ◽  
pp. 1331-1338 ◽  
Author(s):  
Christos Christodoulou-Volos ◽  
Fotios M. Siokis
Keyword(s):  
Stock Market ◽  
Long Range ◽  
Long Range Dependence ◽  
Market Returns ◽  
Stock Market Returns

scholarly journals Bootstrap testing for discontinuities under long-range dependence

2012 ◽  
Vol 105 (1) ◽  
pp. 322-347 ◽  
Author(s):  
Jan Beran ◽  
Yevgen Shumeyko
Keyword(s):  
Long Range ◽  
Long Range Dependence
Sign in / Sign up

Export Citation Format

Share Document